Template-Type: ReDIF-Article 1.0 Author-Name: Farshid Jamshidian Author-X-Name-First: Farshid Author-X-Name-Last: Jamshidian Title: Hedging quantos, differential swaps and ratios Abstract: From first principles, using general no-arbitrage arguments across international markets, differential swaps and a variety of quanto options and futures are evaluated and replicated in closed form by explicit construction of their hedge portfolios, under the assumption of deterministic instantaneous covariances. Journal: Applied Mathematical Finance Pages: 1-20 Issue: 1 Volume: 1 Year: 1994 Keywords: international trading strategies, cross-market hedging, pricing, replication, product and division rules, deterministic covariance, X-DOI: 10.1080/13504869400000001 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Jarrow Author-X-Name-First: Robert Author-X-Name-Last: Jarrow Author-Name: Stuart Turnbull Author-X-Name-First: Stuart Author-X-Name-Last: Turnbull Title: Delta, gamma and bucket hedging of interest rate derivatives Abstract: The paper describes a framework for delta and gamma hedging an interest rate portfolio using a multifactor form of the Heath et al. (1992) model. A formal description of bucket hedging is given along with a discussion of some of the issues surrounding the choice of bucket lengths. Given that a small number of factors can describe the evolution of the term structure, the bucket deltas are defined in terms of these factors. The hedging of corporate bonds is also addressed. Journal: Applied Mathematical Finance Pages: 21-48 Issue: 1 Volume: 1 Year: 1994 Keywords: delta hedging, gamma hedging, bucket hedging, interest rate derivatives, X-DOI: 10.1080/13504869400000002 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000002 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:21-48 Template-Type: ReDIF-Article 1.0 Author-Name: Benjamin Mohamed Author-X-Name-First: Benjamin Author-X-Name-Last: Mohamed Title: Simulations of transaction costs and optimal rehedging Abstract: This paper addresses the issue of hedging options under proportional transaction costs. The Black-Scholes environment assumes frictionless markets in which one can replicate the option payoff exactly by continuous rehedging. However, when transaction costs are involved, frequent rehedging results in the accumulation of transaction costs. Conversely, infrequent hedging results in replication errors. This document attempts to evaluate several rehedging strategies by Monte Carlo simulations. The simulations are constructed so that hedging errors and transaction costs are separated permitting the relative trade-offs to be inspected. Results show that an analytic approximation to a utility maximization approach is both effective and simple to implement. The strategy results in the requirement to hedge to within a dynamic band around the Black-Scholes delta. The band is a function of the option's gamma. Journal: Applied Mathematical Finance Pages: 49-62 Issue: 1 Volume: 1 Year: 1994 Keywords: options, transaction costs, hedging, X-DOI: 10.1080/13504869400000003 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000003 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:49-62 Template-Type: ReDIF-Article 1.0 Author-Name: Alain Bensoussan Author-X-Name-First: Alain Author-X-Name-Last: Bensoussan Author-Name: Michel Crouhy Author-X-Name-First: Michel Author-X-Name-Last: Crouhy Author-Name: Dan Galai Author-X-Name-First: Dan Author-X-Name-Last: Galai Title: Stochastic equity volatility related to the leverage effect Abstract: We propose a general framework to model equity volatility for a firm financed by equity and additional non-equity sources of funds. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities. Second, we show for the first time in the option literature, that instantaneous equity volatility is a solution of a partial differential equation similar to Black-Scholes', although it is non-linear and in general does not have any analytical solution. However, analytical approximations for equity volatility are proposed for different capital structures: (1) equity and debt, (2) equity and warrants, and (3) equity, debt and warrants. They are shown to be very accurate. Journal: Applied Mathematical Finance Pages: 63-85 Issue: 1 Volume: 1 Year: 1994 Keywords: corporate finance, financial structure, leverage effect, option pricing, security valuation, stochastic, volatility, warrants, numerical methods, X-DOI: 10.1080/13504869400000004 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000004 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:63-85 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Hagan Author-X-Name-First: Patrick Author-X-Name-Last: Hagan Author-Name: Diana Woodward Author-X-Name-First: Diana Author-X-Name-Last: Woodward Author-Name: Russel Caflisch Author-X-Name-First: Russel Author-X-Name-Last: Caflisch Author-Name: Joseph Keller Author-X-Name-First: Joseph Author-X-Name-Last: Keller Title: Optimal pricing, use and exploration of uncertain natural resources Abstract: We consider Arrow's model for an economy engaged in consuming a randomly distributed natural resource, and in exploring previously unexplored land to find more of the resource. After modifying the model so that each discovery reveals a random amount of the resource, we use dynamic programming techniques to derive the equations governing optimal rates of exploration, consumption, and pricing of the resource. We analyse these equations asymptotically when the typical amount discovered is small compared with the total amount of the resource, and approximately when the amount is medium or large. In both cases we obtain formulas for the optimal exploration, consumption, and pricing policies. We demonstrate the accuracy of these analytical results by comparing them with numerically-determined exact solutions, and discuss economic implications of these results. Journal: Applied Mathematical Finance Pages: 87-108 Issue: 1 Volume: 1 Year: 1994 Keywords: optimal pricing, dynamic programming, X-DOI: 10.1080/13504869400000005 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000005 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:87-108 Template-Type: ReDIF-Article 1.0 Author-Name: Jesse Jones Author-X-Name-First: Jesse Author-X-Name-Last: Jones Title: Book Reviews Abstract: Journal: Applied Mathematical Finance Pages: 109-110 Issue: 1 Volume: 1 Year: 1994 X-DOI: 10.1080/13504869400000006 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000006 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:109-110 Template-Type: ReDIF-Article 1.0 Author-Name: Jesse Jones Author-X-Name-First: Jesse Author-X-Name-Last: Jones Title: Book Reviews Abstract: Journal: Applied Mathematical Finance Pages: 110-110 Issue: 1 Volume: 1 Year: 1994 X-DOI: 10.1080/13504869400000007 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000007 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:1:p:110-110 Template-Type: ReDIF-Article 1.0 Author-Name: David Porter Author-X-Name-First: David Author-X-Name-Last: Porter Author-Name: Vernon Smith Author-X-Name-First: Vernon Author-X-Name-Last: Smith Title: Stock market bubbles in the laboratory Abstract: Trading at prices above the fundamental value of an asset, i.e. a bubble, has been verified and replicated in laboratory asset markets for the past seven years. To date, only common group experience provides minimal conditions for common investor sentiment and trading at fundamental value. Rational expectations models do not predict the bubble and crash phenomena found in these experimental markets; such models yield only equilibrium predictions and do not articulate a dynamic process that converges to fundamental value with experience. The dynamic models proposed by Caginalp et al. do an excellent job of predicting price patterns after calibration with a previous experimental bubble, given the initial conditions for a new bubble and its controlled fundamental value. Several extensions of this basic laboratory asset market have recently been undertaken which allow for margin buying, short selling, futures contracting, limit price change rules and a host of other changes that could effect price formation in these assets markets. This paper reviews the results of 72 laboratory asset market experiments which include experimental treatments for dampening bubbles that are suggested by rational expectations theory or popular policy prescriptions. Journal: Applied Mathematical Finance Pages: 111-128 Issue: 2 Volume: 1 Year: 1994 Keywords: experimental economics, rational expectations, financial bubbles, futures contracting, insidertrading, dynamical systems, X-DOI: 10.1080/13504869400000008 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000008 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:2:p:111-128 Template-Type: ReDIF-Article 1.0 Author-Name: G. Caginalp Author-X-Name-First: G. Author-X-Name-Last: Caginalp Author-Name: D. Balenovich Author-X-Name-First: D. Author-X-Name-Last: Balenovich Title: Market oscillations induced by the competition between value-based and trend-based investment strategies Abstract: We consider financial market using mathematical models which incorporate an excess demand function that depends not only upon the price but on the price derivative. The classical (value-based) motivation for purchasing the equity is augmented with a trend-based strategy of buying due to rising prices. An analysis (based on money flow and the finiteness of assets) of the supply, demand and price as a function of time leads to a system of ordinary differential equations which is mathematically complete. The numerical study of our equations exhibits overshooting, abrupt reversals and oscillations in prices. We examine our models within the context of real markets and economic laboratory experiments by comparing its predictions with a set of Porter and Smith experiments and with all US stock market “crashes” since 1929. Journal: Applied Mathematical Finance Pages: 129-164 Issue: 2 Volume: 1 Year: 1994 Keywords: market oscillations, trend-based trading strategies, X-DOI: 10.1080/13504869400000009 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:2:p:129-164 Template-Type: ReDIF-Article 1.0 Author-Name: Avellaneda Marco Author-X-Name-First: Avellaneda Author-X-Name-Last: Marco Author-Name: ParaS Antonio Author-X-Name-First: ParaS Author-X-Name-Last: Antonio Title: Dynamic hedging portfolios for derivative securities in the presence of large transaction costs Abstract: We introduce a new class of strategies for hedging derivative securities in the presence of transaction costs assuming lognormal continuous-time prices for the underlying asset. We do not assume necessarily that the payoff is convex as in Leland's work or that transaction costs are small compared to the price changes between portfolio adjustments, as in Hoggardet al.'s work. The type of hedging strategy to be used depends upon the value of the Leland number A= √2/π (k/σ δt, where kis the round-trip transaction cost, σ is the volatility of the underlying asset, and δtis the time-lag between transactions. If A< 1 it is possible to implement modified Black-Scholes delta-hedging strategies, but not otherwise. We propose new hedging strategies that can be used with A≥ 1 to control effectively the hedging risk and transaction costs. These strategies are associated with the solution of a nonlinear obstacleproblem for a diffusion equation with volatility σA=σ √1+A. In these strategies, there are periods in which rehedging takes place after each interval δtand other periods in which a static strategy is required. The solution to the obstacle problem is simple to calculate, and closed-form solutions exist for many problems of practical interest. Journal: Applied Mathematical Finance Pages: 165-194 Issue: 2 Volume: 1 Year: 1994 Keywords: transaction costs, hedging, option pricing, X-DOI: 10.1080/13504869400000010 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000010 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:2:p:165-194 Template-Type: ReDIF-Article 1.0 Author-Name: Feldman Konrad Author-X-Name-First: Feldman Author-X-Name-Last: Konrad Author-Name: Treleaven Philip Author-X-Name-First: Treleaven Author-X-Name-Last: Philip Title: Intelligent systems in finance Abstract: Business sectors ranging from banking and insurance to retail, are benefiting from a whole new generation of 'intelligent' computing techniques. Successful applications include asset forecasting, credit evaluation, fraud detection, portfolio optimization, customer profiling, risk assessment, economic modelling, sales forecasting and retail outlet location. The techniques include expert systems, rule induction, fuzzy logic, neural networks and genetic algorithms, which in many cases are outperforming traditional statistical approaches. Their key features include the ability to recognize and classify patterns, learning from examples, generalization, logical reasoning from premises, adaptability and the ability to handle data which is incomplete, imprecise and noisy. This paper is the first in a series to appear in Applied Mathematical Finance;here we introduce the reader to the basic concepts of intelligent systems, describe their mode of operation and identify applications of the techniques in real world problem domains. Subsequent papers will concentrate on neural networks, genetic algorithms, fuzzy logic and hybrid systems, and will investigate their history and operation more rigorously. Journal: Applied Mathematical Finance Pages: 195-207 Issue: 2 Volume: 1 Year: 1994 Keywords: intelligent systems, neural networks, genetic algorithms, fuzzy logic, hybrid systems, X-DOI: 10.1080/13504869400000011 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869400000011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:1:y:1994:i:2:p:195-207 Template-Type: ReDIF-Article 1.0 Author-Name: U. Cherubini Author-X-Name-First: U. Author-X-Name-Last: Cherubini Author-Name: M. Esposito Author-X-Name-First: M. Author-X-Name-Last: Esposito Title: Options in and on interest rate futures contracts: results from martingale pricing theory Abstract: In this paper we address the theoretical problem of evaluating the quality option embedded in interest rate futures contracts. We use the martingale properties of the prices of interest-rate contingent claims under different probability measures in order to derive solutions for the value of futures and options on futures, accounting for the quality option and assuming a square-root model for the short rate. The futures pricing formula boils down to a simple linear combination of the futures prices of the zero-coupon bonds which constitute the deliverable bonds. A European call option on such a futures can be rewritten as an option on a single futures in which the strike price is 'curved', i.e. it is a decreasing function of the short rate. Journal: Applied Mathematical Finance Pages: 1-16 Issue: 1 Volume: 2 Year: 1995 Keywords: futures, options, quality option, term structure, martingale pricing Cherubini, Esposito, X-DOI: 10.1080/13504869500000001 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:1:p:1-16 Template-Type: ReDIF-Article 1.0 Author-Name: K. Feldman Author-X-Name-First: K. Author-X-Name-Last: Feldman Author-Name: J. Kingdon Author-X-Name-First: J. Author-X-Name-Last: Kingdon Title: Neural networks and some applications to finance Abstract: Neural networks are an established class of non-linear modelling technique. This paper offers an introduction and overview to neural nets with particular emphasis on financial applications. We present a brief history of the subject and provide details on two of the more popular models. In addition we survey some of the recent research issues and algorithms used in applying neural nets to real-world problems, and discuss some of the specific finance applications to which they have been applied. Journal: Applied Mathematical Finance Pages: 17-42 Issue: 1 Volume: 2 Year: 1995 Keywords: neural networks, multi-layer perceptrons, Kohonen networks, backpropagation, finance, X-DOI: 10.1080/13504869500000002 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000002 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:1:p:17-42 Template-Type: ReDIF-Article 1.0 Author-Name: A. Bensoussan Author-X-Name-First: A. Author-X-Name-Last: Bensoussan Author-Name: M. Crouhy Author-X-Name-First: M. Author-X-Name-Last: Crouhy Author-Name: D. Galai Author-X-Name-First: D. Author-X-Name-Last: Galai Title: Stochastic equity volatility related to the leverage effect II: valuation of European equity options and warrants Abstract: We propose a general framework to assess the value of the financial claims issued by the firm, European equity options and warrantsin terms of the stock price. In our framework, the firm's asset is assumed to follow a standard stationary lognormal process with constant volatility. However, it is not the case for equity volatility. The stochastic nature of equity volatility is endogenous, and comes from the impact of a change in the value of the firm's assets on the financial leverage. In a previous paper we studied the stochastic process for equity volatility, and proposed analytic approximations for different capital structures. In this companion paper we derive analytic approximations for the value of European equity options and warrants for a firm financed by equity, debt and warrants. We first present the basic model, which is an extension of the Black-Scholes model, to value corporate securities either as a function of the stock price, or as a function of the firm's total assets. Since stock prices are observable, then for practical purposes, traders prefer to use the stock as the underlying instrument, we concentrate on valuation models in terms of the stock price. Second, we derive an exact solution for the valuation in terms of the stock price of (i) a European call option on the stock of a levered firm, i.e. a European compound call option on the total assets of the firm, (ii) an equity warrant for an all-equity firm, and (iii) an equity warrant for a firm financed by equity and debt. Unfortunately, to compute these solutions we need to specify the function of the stock price in terms of the firm's assets value. In general we are unable to specify this expression, but we propose tight bounds for the value of these options which can be easily computed as a function of the stock price. Our results provide useful extensions of the Black-Scholes model. Journal: Applied Mathematical Finance Pages: 43-60 Issue: 1 Volume: 2 Year: 1995 Keywords: corporate finance, financial structure, leverage effect, option pricing, security valuation, stochastic volatility, warrants, numerical methods, X-DOI: 10.1080/13504869500000003 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000003 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:1:p:43-60 Template-Type: ReDIF-Article 1.0 Author-Name: F. Jamshidian Author-X-Name-First: F. Author-X-Name-Last: Jamshidian Title: A simple class of square-root interest-rate models Abstract: An analytically tractable class of square-root interest-rate models is introduced. Algebraic expressions are found for the drift and volatility parameters of the short rate in terms of initial yield and volatility curves. Explicit formulae are derived for bond, Arrow-Debreu, and European and American bond options. Journal: Applied Mathematical Finance Pages: 61-72 Issue: 1 Volume: 2 Year: 1995 Keywords: square-root process, chi-squared distribution, Riccati equation, yield curve, volatility curve, bond option, X-DOI: 10.1080/13504869500000004 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000004 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:1:p:61-72 Template-Type: ReDIF-Article 1.0 Author-Name: M. Avellaneda Author-X-Name-First: M. Author-X-Name-Last: Avellaneda Author-Name: A. Levy Author-X-Name-First: A. Author-X-Name-Last: Levy Author-Name: A. ParAS Author-X-Name-First: A. Author-X-Name-Last: ParAS Title: Pricing and hedging derivative securities in markets with uncertain volatilities Abstract: We present a model for pricing and hedging derivative securities and option portfolios in an environment where the volatility is not known precisely, but is assumed instead to lie between two extreme values σminand σmax. These bounds could be inferred from extreme values of the implied volatilities of liquid options, or from high-low peaks in historical stock- or option-implied volatilities. They can be viewed as defining a confidence interval for future volatility values. We show that the extremal non-arbitrageable prices for the derivative asset which arise as the volatility paths vary in such a band can be described by a non-linear PDE, which we call the Black-Scholes-Barenblatt equation. In this equation, the 'pricing' volatility is selected dynamically from the two extreme values, σmin, σmax, according to the convexity of the value-function. A simple algorithm for solving the equation by finite-differencing or a trinomial tree is presented. We show that this model captures the importance of diversification in managing derivatives positions. It can be used systematically to construct efficient hedges using other derivatives in conjunction with the underlying asset. Journal: Applied Mathematical Finance Pages: 73-88 Issue: 2 Volume: 2 Year: 1995 Keywords: hedging, volatility risk, X-DOI: 10.1080/13504869500000005 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000005 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:2:p:73-88 Template-Type: ReDIF-Article 1.0 Author-Name: J. Kingdon Author-X-Name-First: J. Author-X-Name-Last: Kingdon Author-Name: K. Feldman Author-X-Name-First: K. Author-X-Name-Last: Feldman Title: Genetic algorithms and applications to finance Abstract: Genetic algorithms are a class of probabilistic optimization techniques that have proved useful in a wide variety of problem domains. This paper offers an introduction and overview to genetic algorithms and examines some of the finance-related applications to which the technique has been applied. Journal: Applied Mathematical Finance Pages: 89-116 Issue: 2 Volume: 2 Year: 1995 Keywords: optimization, genetic algorithms, evolutionary algorithms, evolutionary computing, finance, X-DOI: 10.1080/13504869500000006 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000006 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:2:p:89-116 Template-Type: ReDIF-Article 1.0 Author-Name: T. J. Lyons Author-X-Name-First: T. J. Author-X-Name-Last: Lyons Title: Uncertain volatility and the risk-free synthesis of derivatives Abstract: To price contingent claims in a multidimensional frictionless security market it is sufficient that the volatility of the security process is a known function of price and time. In this note we introduce optimal and risk-free strategies for intermediaries in such markets to meet their obligations when the volatility is unknown, and is only assumed to lie in some convex region depending on the prices of the underlying securities and time. Our approach is underpinned by the theory of totally non-linear parabolic partial differential equations (Krylov and Safanov, 1979; Wang, 1992) and the non-stochastic approach to Ito's formation first introduced by Follmer (1981a,b). In these more general conditions of unknown volatility, the optimal risk-free trading strategy will, necessarily, produce an unpredictable surplus over the minimum assets required at any time to meet the liabilities. This surplus, which could be released to the intermediary or to the client, is not required to meet the contingent claim. One sees that the effect of unknown volatility is the creation of a 'with profits' policy, where a premium is paid at the beginning, the contingent claim is collected at the terminal time, but that in addition an unpredictable surplus available as well. The risk-free initial premium required to meet the contingent claim is given by the solution to the Dirichlet problem for a totally non-linear parabolic equation of the Pucci-Bellman type. The existence of a risk-free strategy starting with this minimum sum is dependent upon theorems ensuring the regularity of the solution and upon a non-probabilistic understanding of Ito's change of variable formulae. To illustrate the ideas we give a very simple example of a one-dimensional barrier option where the maximum Black-Scholes price of the option over different fixed values for the volatility lying in an interval always underestimates the risk-free 'price' under the assumption that the volatility can vary within the same interval. This paper puts together rather standard mathematical ideas. However, the author hopes that the overall result is more than the sum of its parts. The ability to hedge under conditions of uncertain volatility seems to be of considerable practical importance. In addition it would be interesting if these ideas explained some features in the design of existing contracts. Journal: Applied Mathematical Finance Pages: 117-133 Issue: 2 Volume: 2 Year: 1995 Keywords: volatility, derivative contract, random volatility, Pucci-Bellman equation, Black-Scholes Formula, X-DOI: 10.1080/13504869500000007 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000007 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:2:p:117-133 Template-Type: ReDIF-Article 1.0 Author-Name: Rob Bauer Author-X-Name-First: Rob Author-X-Name-Last: Bauer Author-Name: Fred Nieuwland Author-X-Name-First: Fred Author-X-Name-Last: Nieuwland Title: A multiplicative model for volume and volatility Abstract: We first present prima facie evidence for the predictions generated by the mixture of distributions hypothesis, using daily German stock returns and their corresponding daily trading volumes and number of trades. These last two variables are used as proxies for the stochastic rate of information arrival when one wishes to explain GARCH effects by adhering to the mixture of distributions hypothesis. We show that there is no need for these proxies when the stochastic rate of information arrival follows an inverted gamma distribution. Daily trading volume and the daily number of trades, however, empirically provide an explanation for the occurrence of conditional heteroskedasticity of the GARCH form. We estimate several specifications where daily trading volume is included in the conditional variance equation additively and multiplicatively. The new multiplicative specification clearly outperforms the additive specification. Journal: Applied Mathematical Finance Pages: 135-154 Issue: 3 Volume: 2 Year: 1995 X-DOI: 10.1080/13504869500000008 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000008 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:3:p:135-154 Template-Type: ReDIF-Article 1.0 Author-Name: J. L. Knight Author-X-Name-First: J. L. Author-X-Name-Last: Knight Author-Name: S. E. Satchell Author-X-Name-First: S. E. Author-X-Name-Last: Satchell Author-Name: K. C. Tran Author-X-Name-First: K. C. Author-X-Name-Last: Tran Title: Statistical modelling of asymmetric risk in asset returns Abstract: The purpose of this article is to provide a straightforward model for asset returns which captures the fundamental asymmetry in upward versus downward returns. We model this feature by using scale gamma distributions for the conditional distributions of positive and negative returns. By allowing the parameters for positive returns to differ from parameters for negative returns we can test the hypothesis of symmetry. Some applications of this process to expected utility and semi-variance calculations are considered. Finally we estimate the model using daily UK FT100 index and Futures data. Journal: Applied Mathematical Finance Pages: 155-172 Issue: 3 Volume: 2 Year: 1995 Keywords: asymmetric returns, FT 100, semi-variance, scale gamma distribution, X-DOI: 10.1080/13504869500000009 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:3:p:155-172 Template-Type: ReDIF-Article 1.0 Author-Name: P. Carr Author-X-Name-First: P. Author-X-Name-Last: Carr Title: Two extensions to barrier option valuation Abstract: We first present a brief but essentially complete survey of the literature on barrier option pricing. We then present two extensions of European up-and-out call option valuation. The first allows for an initial protection period during which the option cannot be knocked out. The second considers an option which is only knocked out if a second asset touches an upper barrier. Closed form solutions, detailed derivations, and the economic rationale for both types of options are provided. Journal: Applied Mathematical Finance Pages: 173-209 Issue: 3 Volume: 2 Year: 1995 Keywords: option pricing, exotic options, X-DOI: 10.1080/13504869500000010 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000010 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:3:p:173-209 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Peszek Author-X-Name-First: Robert Author-X-Name-Last: Peszek Title: PDE Models for Pricing Stocks and Options With Memory Feedback Abstract: This paper describes partial differential equation (PDE) models for pricing stocks and options in the presence of memory feedback. Of interest are economic situations in which the stock (option) value at time T depends on some type of average of its past values. Derived PDEs resemble viscous Burgers' equations. Journal: Applied Mathematical Finance Pages: 211-224 Issue: 4 Volume: 2 Year: 1995 Keywords: Burgers', equation, memory feedback, trading strategy, pricing, X-DOI: 10.1080/13504869500000011 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:4:p:211-224 Template-Type: ReDIF-Article 1.0 Author-Name: G. Caginalp Author-X-Name-First: G. Author-X-Name-Last: Caginalp Author-Name: G. Constantine Author-X-Name-First: G. Author-X-Name-Last: Constantine Title: Statistical inference and modelling of momentum in stock prices Abstract: The following results are obtained, (i) It is possible to obtain a time series of market data {y(t)} in which the fluctuations in fundamental value have been compensated for. An objective test of the efficient market hypothesis (EMH), which would predict random correlations about a constant value, is thereby possible, (ii) A time series procedure can be used to determine the extent to which the differences in the data and the moving averages are significant. This provides a model of the form y(t)-y(t-l)=0.5{y(t- l)-y(t-2)}+ε(t)+0.8ε(r-1) where ε(t) is the error at time t, and the coefficients 0.5 and 0.8 are determined from the data. One concludes that today's price is not a random perturbation from yesterday's; rather, yesterday's rate of change is a significant predictor of today's rate of change. This confirms the concept of momentum that is crucial to market participants. (iii) The model provides out-of-sample predictions that can be tested statistically. (iv) The model and coefficients obtained in this way can be used to make predictions on laboratory experiments to establish an objective and quantitative link between the experiments and the market data. These methods circumvent the central difficulty in testing market data, namely, that changes in fundamentals obscure intrinsic trends and autocorrelations. This procedure is implemented by considering the ratio of two similar funds (Germany and Future Germany) with the same manager and performing a set of statistical tests that have excluded fluctuations in fundamental factors. For the entire data of the first 1149 days beginning with the introduction of the latter fund, a standard runs test indicates that the data is 29 standard deviations away from that which would be expected under a hypothesis of random fluctuations about the fundamental value. This and other tests provide strong evidence against the efficient market hypothesis and in favour of autocorrelations in the data. An ARIMA time series finds strong evidence (9.6 and 21.6 standard deviations in the two coefficients) that the data is described by a model that involves the first difference, indicating that momentum is the significant factor. The first quarter's data is used to make out-of-sample predictions for the second quarter with results that are significant to 3 standard deviations. Finally, the ARIMA model and coefficients are used to make predictions on laboratory experiments of Porter and Smith in which the intrinsic value is clear. The model's forecasts are decidedly more accurate than that of the null hypothesis of random fluctuations about the fundamental value. Journal: Applied Mathematical Finance Pages: 225-242 Issue: 4 Volume: 2 Year: 1995 Keywords: stock price momentum, ARIMA, statistical modelling of financial instruments, closed end funds, X-DOI: 10.1080/13504869500000012 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000012 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:4:p:225-242 Template-Type: ReDIF-Article 1.0 Author-Name: J. Shaw Author-X-Name-First: J. Author-X-Name-Last: Shaw Author-Name: E. O. Thorp Author-X-Name-First: E. O. Author-X-Name-Last: Thorp Author-Name: W. T. Ziemba Author-X-Name-First: W. T. Author-X-Name-Last: Ziemba Title: Risk arbitrage in the Nikkei put warrant market of 1989-1990 Abstract: This paper discusses the Nikkei put warrant market in Toronto and New York during 1989-1990. Three classes of long term American puts were traded which when evaluated in yen are ordinary, product and exchange asset puts, respectively. Type I do not involve exchange rates for yen investors. Type II, called quantos, fix in advance the exchange rate to be used on expiry in the home currency. Type III evaluate the strike and spot prices of the Nikkei Stock Average in the home currency rather than in yen. For typically observed parameters, type I are theoretically more valuable than type II which in turn are more valuable than type III. In late 1989 and early 1990 there were significant departures from fair values in various markets. This was a market with a set of complex financial instruments that even sophisticated investors needed time to learn about to price properly. Investors in Canada were willing to buy puts at far more than fair value based on historical volatility. In addition, US investors overpriced type II puts fixed in dollars rather than the type I's in yen. This led to cross border and US traded (on the same exchange) low risk hedges. The market's convergence to efficiency (that is, all puts priced within transaction cost bands) took about one month after the introduction of the US puts in early 1990 leading to significant profits for the hedgers. Journal: Applied Mathematical Finance Pages: 243-272 Issue: 4 Volume: 2 Year: 1995 Keywords: option mispricing, cross-border trading, Nikkei stock exchange, Shaw et al, X-DOI: 10.1080/13504869500000013 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000013 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:4:p:243-272 Template-Type: ReDIF-Article 1.0 Author-Name: R. C. Heynen Author-X-Name-First: R. C. Author-X-Name-Last: Heynen Author-Name: H. M. Kat Author-X-Name-First: H. M. Author-X-Name-Last: Kat Title: Lookback options with discrete and partial monitoring of the underlying price Abstract: We show that in the world of Black and Scholes (1973) lookback options where the underlying price is monitored discretely instead of continuously can be priced in semi-closed form. We derive pricing formulas for a variety of full and partial lookback options, where monitoring takes place at not necessarily equally-spaced points in time. Analysis of the results shows that monitoring the underlying price discretely instead of continuously may have a significant effect on the prices of lookback options but does not introduce new hedging problems. Journal: Applied Mathematical Finance Pages: 273-284 Issue: 4 Volume: 2 Year: 1995 Keywords: exotic options, lookback options, risk neutral valuation, multivariate normal distribution, numerical integration, X-DOI: 10.1080/13504869500000014 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869500000014 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:2:y:1995:i:4:p:273-284 Template-Type: ReDIF-Article 1.0 Author-Name: S. Ninomiya Author-X-Name-First: S. Author-X-Name-Last: Ninomiya Author-Name: S. Tezuka Author-X-Name-First: S. Author-X-Name-Last: Tezuka Title: Toward real-time pricing of complex financial derivatives Abstract: In this paper, we investigate the feasibility of using low-discrepancy sequences to allow complex derivatives, such as mortgage-backed securities (MBSs) and exotic options, to be calculated considerably faster than is possible by using conventional Monte Carlo methods. In our experiments, we examine classical classes of low-discrepancy sequences, such as Halton, Sobol', and Faure sequences, as well as the very recent class called generalized Niederreiter sequences, in the light of the actual convergence rate of numerical integration with practical numbers of dimensions. Our results show that for the problems of pricing financial derivatives that we tested: (1) generalized Niederreiter sequences perform markedly better than both classical sequences and Monte Carlo methods; and (2) classical low-discrepancy sequences often perform worse than Monte Carlo methods. Finally, we discuss several important research issues from both practical and theoretical viewpoints. Journal: Applied Mathematical Finance Pages: 1-20 Issue: 1 Volume: 3 Year: 1996 Keywords: low-discrepancy sequences, generalized Niederreiter sequences, Faure sequences, Sobol' sequences, financial derivatives, X-DOI: 10.1080/13504869600000001 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Avellaneda Author-X-Name-First: Marco Author-X-Name-Last: Avellaneda Author-Name: Antonio ParAS Author-X-Name-First: Antonio Author-X-Name-Last: ParAS Title: Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model Abstract: We present an algorithm for hedging option portfolios and custom-tailored derivative securities, which uses options to manage volatility risk. The algorithm uses a volatility band to model heteroskedasticity and a non- linear partial differential equation to evaluate worst-case volatility scenarios for any given forward liability structure. This equation gives sub-additive portfolio prices and hence provides a natural ordering of prefer- ences in terms of hedging with options. The second element of the algorithm consists of a portfolio optim- ization taking into account the prices of options available in the market. Several examples are discussed, including possible applications to market-making in equity and foreign-exchange derivatives. Journal: Applied Mathematical Finance Pages: 21-52 Issue: 1 Volume: 3 Year: 1996 Keywords: Uncertain volatility, dynamic hedging, hedging with options, X-DOI: 10.1080/13504869600000002 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000002 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:21-52 Template-Type: ReDIF-Article 1.0 Author-Name: Ian Cooper Author-X-Name-First: Ian Author-X-Name-Last: Cooper Author-Name: Marcel Martin Author-X-Name-First: Marcel Author-X-Name-Last: Martin Title: Default risk and derivative products Abstract: The modelling of default risk in debt securities involves making assumptions about the stochastic process driv- ing default, the process generating the write-down in default, and risk-free interest rates. Three generic approaches have been used. The first relies on modelling the value of the assets on which the debt is written. The second involves modelling default as an arrival process. The third involves directly modelling the interest rate spreads to which default gives rise. Each of these approaches may be applied to the impact of default risk on derivative products such as swaps and options. One application is to the valuation of derivative products that may default. The other is to the new class of 'credit derivatives' that represent derivative products written on credit risk. Journal: Applied Mathematical Finance Pages: 53-70 Issue: 1 Volume: 3 Year: 1996 Keywords: default risk, credit risk, risky debt, derivative products, X-DOI: 10.1080/13504869600000003 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000003 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:53-70 Template-Type: ReDIF-Article 1.0 Author-Name: O. Scaillet Author-X-Name-First: O. Author-X-Name-Last: Scaillet Title: Compound and exchange options in the affine term structure model Abstract: We present explicit formulae allowing us to price compound and exchange options in the framework of the affine term structure model. The various proposed options deal with discount bonds, coupon bonds and yields. A probabilistic approach is adopted in order to find closed-form pricing formulae. We also give some numerical examples of their use in credit loans. Journal: Applied Mathematical Finance Pages: 75-92 Issue: 1 Volume: 3 Year: 1996 Keywords: term structure, compound option, exchange option, affine model, X-DOI: 10.1080/13504869600000004 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000004 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:1:p:75-92 Template-Type: ReDIF-Article 1.0 Author-Name: Farshid Jamshidian Author-X-Name-First: Farshid Author-X-Name-Last: Jamshidian Title: Bond, futures and option evaluation in the quadratic interest rate model Abstract: This paper develops the quadratic interest-rate model of Beaglehole and Tenney in detail. For the quadratic model as well as the multifactor Cox-Ingersoll-Ross square-root model, explicit pricing formulae in terms of one-dimensional integrals of elementary functions are given for bond options, bond exchange options, caps, options on bond futures and forward contracts, and futures delivery options. For the quadratic model, certain forward and transport equations are found that explicitly determine the dynamics of the term structure in terms of initial yield and volatility curves. These option-pricing formulae are thus determined in term of the initial curves. Some shortcomings of the model are identified. New formulae for some distributions and their truncated moments are also derived. Journal: Applied Mathematical Finance Pages: 93-115 Issue: 2 Volume: 3 Year: 1996 Keywords: principal value integral, noncentral chi-squared distribution, forward risk adjustment, forward and transport equations, yield curve calibration, X-DOI: 10.1080/13504869600000005 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000005 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:2:p:93-115 Template-Type: ReDIF-Article 1.0 Author-Name: Haim Levy Author-X-Name-First: Haim Author-X-Name-Last: Levy Title: Investment diversification and investment specialization and the assumed holding period Abstract: Optimum mean-variance (M-V) investment diversification strategies are analysed as a function of alternative investment horizons. For almost all possible one-period correlations across assets, it is found that as the investment horizon increases, the correlations approach zero and the M-V investor tends to specialize in one asset-the one with the lowest value Ai when, Ai ***, which implies in most cases specialization in the lowest mean asset. The lowest mean asset dominates because the multiperiod variance increases faster for assets with high mean returns and because of the possibility of borrowing and lending at the risk-free interest rate. This strategy is contrary to professional investment advice, which generally asserts that, for longer investment horizons, the investor can achieve diversification across time by investing primarily in equities which are characterized by relatively higher mean returns. Similar results hold when the M-V rule is relaxed and the investor maximizes expected utility (myopic) when portfolio revisions are allowed. Journal: Applied Mathematical Finance Pages: 117-134 Issue: 2 Volume: 3 Year: 1996 Keywords: Investment horizon, multiperiod variance, multiperiod correlation, X-DOI: 10.1080/13504869600000006 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000006 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:2:p:117-134 Template-Type: ReDIF-Article 1.0 Author-Name: Fabio Mercurio Author-X-Name-First: Fabio Author-X-Name-Last: Mercurio Author-Name: Ton Vorst Author-X-Name-First: Ton Author-X-Name-Last: Vorst Title: Option pricing with hedging at fixed trading dates Abstract: We introduce trading restrictions in the well known Black-Scholes model and Cox-Ross-Rubinstein model, in the sense that hedging is only allowed at some fixed trading dates. As a consequence, the financial market is incomplete in both modified models. Applying Schweizer's (and Schal's) variance-optimal criterion for pricing and hedging general claims, we first analyse the dynamic consistency of the strategies which minimize the variance of the total loss due to hedging a given claim. Then we establish some convergence results, when the number of trading dates is either kept fixed or increases to infinity. Journal: Applied Mathematical Finance Pages: 135-158 Issue: 2 Volume: 3 Year: 1996 X-DOI: 10.1080/13504869600000007 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000007 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:2:p:135-158 Template-Type: ReDIF-Article 1.0 Author-Name: Michel Habib Author-X-Name-First: Michel Author-X-Name-Last: Habib Author-Name: Narayan Naik Author-X-Name-First: Narayan Author-X-Name-Last: Naik Title: Models of information aggregation in financial markets: a review Abstract: This article reviews static and dynamic models of information aggregation in the literature. It highlights the key assumptions these models make, the results they obtain and the issues that still need to be explored to further our understanding of information aggregation in financial markets. Journal: Applied Mathematical Finance Pages: 159-166 Issue: 2 Volume: 3 Year: 1996 Keywords: rational expectations equilibrium, incomplete markets, X-DOI: 10.1080/13504869600000008 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000008 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:2:p:159-166 Template-Type: ReDIF-Article 1.0 Author-Name: K. G. Nyborg Author-X-Name-First: K. G. Author-X-Name-Last: Nyborg Title: The use and pricing of convertible bonds Abstract: This paper provides an overview of the main results of the literature on pricing convertible bonds. It covers simple convertible bonds which are non-callable and can be converted only at maturity as well as more complicated callable and puttable convertible bonds under stochastic interest rates. The paper also reviews the main results in the literature on why firms issue convertible bonds. The two most often cited rationales for issuing convertible bonds - as delayed equity, and to sweeten debt - are discussed in the context of both asymmetric information and agency models of capital structure. Finally, the paper provides some thoughts on incorporating strategic issues into the pricing of convertible bonds. Journal: Applied Mathematical Finance Pages: 167-190 Issue: 3 Volume: 3 Year: 1996 Keywords: risky/risk-free assets, call and put features, debt pricing, convertible debt, adverse selection, moral hazard, X-DOI: 10.1080/13504869600000009 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:3:p:167-190 Template-Type: ReDIF-Article 1.0 Author-Name: C. N. Bagley Author-X-Name-First: C. N. Author-X-Name-Last: Bagley Author-Name: U. Yaari Author-X-Name-First: U. Author-X-Name-Last: Yaari Title: Financial leverage strategy with transaction costs Abstract: This paper offers a class of diffusion models that mimic the firm's pecking order behaviour and are designed to optimize an intertemporal leverage strategy in the presence of refinancing transaction costs. The proposed class of models is compatible with traditional static tradeoff theories and can be used to recast those theories in a dynamic framework by superimposing refinancing costs. We derive analytical expressions for the parameters of an optimal leverage strategy with exogenous refinancing limits, including the minimum cost of capital in a stochastic dynamic framework with transaction costs, the target values to which the leverage should be readjusted when the limits are reached, and the mean leverage implied by the optimal strategy. Our class of models enriches the pecking order theory and provides a quantitative framework for its implementation as a decision tool. It also provides additional hypotheses for empirical validation of that theory. Symmetrically, our results show the importance of dynamic factors in designing and interpreting empirical tests of static tradeoff theories. Journal: Applied Mathematical Finance Pages: 191-208 Issue: 3 Volume: 3 Year: 1996 Keywords: dynamic diffusion model, financial leverage estimation, financial leverage strategy, pecking order theory, X-DOI: 10.1080/13504869600000010 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000010 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:3:p:191-208 Template-Type: ReDIF-Article 1.0 Author-Name: J. A. Nielsen Author-X-Name-First: J. A. Author-X-Name-Last: Nielsen Author-Name: K. Sandmann Author-X-Name-First: K. Author-X-Name-Last: Sandmann Title: The pricing of Asian options under stochastic interest rates Abstract: The purpose of this paper is to analyse the effect of stochastic interest rates on the pricing of Asian options. It is shown that a stochastic, in contrast to a deterministic, development of the term structure of interest rates has a significant influence. The price of the underlying asset, e.g. a stock or oil, and the prices of bonds are assumed to follow correlated two-dimensional Ito processes. The averages considered in the Asian options are calculated on a discrete time grid, e.g. all closing prices on Wednesdays during the lifetime of the contract. The value of an Asian option will be obtained through the application of Monte Carlo simulation, and for this purpose the stochastic processes for the basic assets need not be severely restricted. However, to make comparison with published results originating from models with deterministic interest rates, we will stay within the setting of a Gaussian framework. Journal: Applied Mathematical Finance Pages: 209-236 Issue: 3 Volume: 3 Year: 1996 Keywords: Asian options, forward risk adjusted measure, Monte Carlo simulation, X-DOI: 10.1080/13504869600000011 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:3:p:209-236 Template-Type: ReDIF-Article 1.0 Author-Name: M. Rutkowski Author-X-Name-First: M. Author-X-Name-Last: Rutkowski Title: Valuation and hedging of contingent claims in the HJM model with deterministic volatilities Abstract: The aim of the present paper is mostly expository, namely, we intend to provide a concise presentation of arbitrage pricing and hedging of European contingent claims within the Heath, Jarrow and Morton frame-work introduced in Heath et al. (1992) under deterministic volatilities. Such a special case of the HJM model, frequently referred to as the Gaussian HJM model, was studied among others in Amin and Jarrow (1992), Jamshidian (1993), Brace and Musiela (1994a, 1994b). Here, we focus mainly on the partial differential equations approach to the valuation and hedging of derivative securities in the HJM framework. For the sake of completeness, the risk neutral methodology (more specifically, the forward measure technique) is also exposed. Journal: Applied Mathematical Finance Pages: 237-267 Issue: 3 Volume: 3 Year: 1996 Keywords: term structure of interest rates, bond option, interest rate derivatives, X-DOI: 10.1080/13504869600000012 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000012 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:3:p:237-267 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rita Bacinello Author-X-Name-First: Anna Rita Author-X-Name-Last: Bacinello Author-Name: Fulvio Ortu Author-X-Name-First: Fulvio Author-X-Name-Last: Ortu Author-Name: Patrizia Stucchi Author-X-Name-First: Patrizia Author-X-Name-Last: Stucchi Title: Valuation of sinking-fund bonds in the Vasicek and CIR frameworks*Financial support from Murst Fondo 40% on 'Modelli di struttura a termine dei tassi d'interesse' is gratefully acknowledged. Abstract: In a sinking-fund bond, the issuer is required to retire portions of the bond prior to maturity, with the option of doing so either by calling the bonds by lottery, or by buying them back at their market value. This paper discusses the valuation of a default-free sinking-fund bond issue in the Vasicek (1977) and, alternatively, the Cox, Ingersoll and Ross (CIR) (1985) frameworks. We show in particular that, calling the bond issue without the delivery option 'corresponding serial', and the one without the prepayment feature 'corresponding coupon', under no-arbitrage a sinking-fund bond can be priced either in terms of the corresponding coupon bond and a bond call option, or in terms of the corresponding serial and a bond put option. We also present a detailed comparative-statics analysis of our valuation model, where we show that a sinking-fund bond has a stochastic duration intermediate between the ones of the corresponding serial and coupon bonds. We argue that such a feature gives a further rational for the presence of the delivery option. Moreover, we compare our results with the ones of Ho (1985), who has previously discussed the valuation problem under scrutiny. Journal: Applied Mathematical Finance Pages: 269-394 Issue: 4 Volume: 3 Year: 1996 Keywords: sinking-fund bonds, delivery option, term structure models, Vasicek, CIR, X-DOI: 10.1080/13504869600000013 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000013 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:4:p:269-394 Template-Type: ReDIF-Article 1.0 Author-Name: Rudiger Frey Author-X-Name-First: Rudiger Author-X-Name-Last: Frey Author-Name: Daniel Sommer Author-X-Name-First: Daniel Author-X-Name-Last: Sommer Title: A systematic approach to pricing and hedging international derivatives with interest rate risk: analysis of international derivatives under stochastic interest rates Abstract: This paper deals with the valuation and the hedging of non-path-dependent European options on one or several underlying assets in a model of an international economy allowing for both, interest rate risk and exchange rate risk. Using martingale theory and, in particular, the change of numeraire technique we provide a unified and easily applicable approach to pricing and hedging exchange options on stocks, bonds, futures, interest rates and exchange rates. We also cover the pricing and hedging of compound exchange options. Journal: Applied Mathematical Finance Pages: 295-317 Issue: 4 Volume: 3 Year: 1996 Keywords: option pricing and hedging, interest rate risk, exchange rate risk, change of numeraire, X-DOI: 10.1080/13504869600000014 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000014 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:4:p:295-317 Template-Type: ReDIF-Article 1.0 Author-Name: Dietmar Leisen Author-X-Name-First: Dietmar Author-X-Name-Last: Leisen Author-Name: Matthias Reimer Author-X-Name-First: Matthias Author-X-Name-Last: Reimer Title: Binomial models for option valuation - examining and improving convergence Abstract: Binomial models, which describe the asset price dynamics of the continuous-time model in the limit, serve for approximate valuation of options, especially where formulas cannot be derived analytically due to properties of the considered option type. To evaluate results, one inevitably must understand the convergence properties. In the literature we find various contributions proving convergence of option prices. We examine convergence behaviour and convergence speed. Unfortunately, even in the case of European call options, distorted results occur when calculating prices along the iteration of tree refinements. These convergence patterns are examined and order of convergence one is proven for the Cox-Ross-Rubinstein model as well as for two alternative tree parameter selections from the literature. Furthermore, we define new binomial models, where the calculated option prices converge smoothly to the Black-Scholes solution, and we achieve order of convergence two with much smaller initial error. Notably, only the formulas to determine the up- and down-factors change. Finally, following a recent approach from the literature, all tree approaches are compared with respect to speed and accuracy, calculating the relative root-mean-squared error of approximate option values for a sample of randomly selected parameters across a set of refinements. Here, on average, the same degree of accuracy is achieved 1400 times faster with the new binomial models. We also give some insights into the peculiarities in the valuation of the American put option. Inspecting the numerical results, the approximation of American-type options with the new models exhibits order of convergence one, but with a smaller initial error than with previously existing binomial models, giving the same accuracy on average ten-times faster than previous binomial methods. Journal: Applied Mathematical Finance Pages: 319-346 Issue: 4 Volume: 3 Year: 1996 Keywords: binomial model, option valuation, order of convergence, convergence pattern, X-DOI: 10.1080/13504869600000015 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000015 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:4:p:319-346 Template-Type: ReDIF-Article 1.0 Author-Name: Mark Britten-Jones Author-X-Name-First: Mark Author-X-Name-Last: Britten-Jones Author-Name: Anthony Neuberger Author-X-Name-First: Anthony Author-X-Name-Last: Neuberger Title: Arbitrage pricing with incomplete markets Abstract: This paper presents a new arbitrage-free approach to the pricing of derivatives, when the price process of the underlying security does not conform to the standard assumptions. In comparision to the Black-Scholes price process we relax the requirements of i) continuity; ii) constant volatility; and iii) infinite trading possibilities. We retain the assumption that the average volatility of price changes over the option's life is known, and we require that price jumps not be greater than some specified size. With only these assumptions we show that the no-arbitrage bound on a European call option's value approaches the Black-Scholes price as the maximum jump size approaches zero. We present a simple numerical method for the calculation of option pricing bounds for any specified maximum jump size, and discuss implications of our model for hedging, and the estimation of volatility. Journal: Applied Mathematical Finance Pages: 347-363 Issue: 4 Volume: 3 Year: 1996 Keywords: derivatives, arbitrage, price jumps, X-DOI: 10.1080/13504869600000016 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869600000016 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:3:y:1996:i:4:p:347-363 Template-Type: ReDIF-Article 1.0 Author-Name: M. A. H. Dempster Author-X-Name-First: M. A. H. Author-X-Name-Last: Dempster Author-Name: J. P. Hutton Author-X-Name-First: J. P. Author-X-Name-Last: Hutton Title: Fast numerical valuation of American, exotic and complex options Abstract: The purpose of this paper is to present evidence in support of the hypothesis that fast, accurate and parametrically robust numerical valuation of a wide range of derivative securities can be achieved by use of direct numerical methods in the solution of the associated PDE problems. Specifically, linear programming methods for American vanilla and exotic options, and explicit methods for a three stochastic state variable problem (a multi-period terminable differential swap) are explored and promising numerical results are discussed. The resulting value surface gives, simultaneously, valuation for many maturities and underlying prices, and the parameters required for risk analysis. Journal: Applied Mathematical Finance Pages: 1-20 Issue: 1 Volume: 4 Year: 1997 Keywords: Options, Swaps, Parabolic Pdes, Direct Numerical Methods, Linear Programming, X-DOI: 10.1080/135048697334809 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334809 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Hyungsok Ahn Adviti Author-X-Name-First: Hyungsok Ahn Author-X-Name-Last: Adviti Author-Name: Glen Swindle Author-X-Name-First: Glen Author-X-Name-Last: Swindle Title: Misspecified asset price models and robust hedging strategies Abstract: The Black-Scholes theory of option pricing requires a perfectly specified model for the underlying price. Frequently this is taken to be a geometric Brownian motion with a constant, known volatility. In practice, parameters such as the volatility are not known precisely, but are simply estimates from either historical prices or implied volatilities. This paper presents a method for constructing hedging (trading) strategies which are 'robust' to misspecifications of the asset price model. Journal: Applied Mathematical Finance Pages: 21-36 Issue: 1 Volume: 4 Year: 1997 Keywords: Incomplete Markets, Option Hedging Strategies, X-DOI: 10.1080/135048697334818 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334818 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:1:p:21-36 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Avellaneda Author-X-Name-First: Marco Author-X-Name-Last: Avellaneda Author-Name: Craig Friedman Author-X-Name-First: Craig Author-X-Name-Last: Friedman Author-Name: Richard Holmes Author-X-Name-First: Richard Author-X-Name-Last: Holmes Author-Name: Dominick Samperi Author-X-Name-First: Dominick Author-X-Name-Last: Samperi Title: Calibrating volatility surfaces via relative-entropy minimization Abstract: A framework for calibrating a pricing model to a prescribed set of options prices quoted in the market is presented. Our algorithm yields an arbitrage-free diffusion process that minimizes the Kullback-Leibler relative entropy distance to a prior diffusion. It consists in solving a constrained (minimax) optimal control problem using a finite-difference scheme for a Bellman parabolic equation combined with a gradient-based optimization routine. The number of unknowns to be solved for in the optimization step is equal to the number of option prices that need to be calibrated, and is independent of the mesh-size used for the scheme. This results in an efficient, non-parametric calibration method that can match an arbitrary number of option prices to any desired degree of accuracy. The algorithm can be used to interpolate, both in strike and expiration date, between implied volatilities of traded options and to price exotics. The stability and qualitative properties of the computed volatility surface are discussed, including the effect of the Bayesian prior on the shape of the surface and on the implied volatility smile/skew. The method is illustrated by calibrating to market prices of Dollar-Deutschmark over-the-counter options and computing interpolated implied-volatility curves. Journal: Applied Mathematical Finance Pages: 37-64 Issue: 1 Volume: 4 Year: 1997 Keywords: Option Pricing, Implied Volatility Surface, Calibration, Relative Entropy, Stochastic, Control, Volatility, Smile, Skew, X-DOI: 10.1080/135048697334827 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334827 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:1:p:37-64 Template-Type: ReDIF-Article 1.0 Author-Name: Ralf Korn Author-X-Name-First: Ralf Author-X-Name-Last: Korn Title: Some applications of L2-hedging with a non-negative wealth process Abstract: We consider the problem of L2-hedging of contingent claims in diffusion type models for securities markets. In contrast to a recent paper of Schweizer (1994) we insist on a non-negative wealth process corresponding to the optimal hedge portfolio. For this reason the usual projection methods cannot be applied. We give some applications of L2-hedging in this setting including hedging under constraints, a problem of approximating the wealth process of a richer investor and a mean-variance version of it. Journal: Applied Mathematical Finance Pages: 65-79 Issue: 1 Volume: 4 Year: 1997 Keywords: Hedging, Portfolio Optimization, Continuous Trading, Complete, Incomplete, Markets, X-DOI: 10.1080/135048697334836 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334836 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:1:p:65-79 Template-Type: ReDIF-Article 1.0 Author-Name: Yingzi Zhu Author-X-Name-First: Yingzi Author-X-Name-Last: Zhu Author-Name: Marco Avellaneda Author-X-Name-First: Marco Author-X-Name-Last: Avellaneda Title: An E-ARCH model for the term structure of implied volatility of FX options Abstract: We construct a statistical model for the term-structure of implied volatilities of currency options based on daily historical data for 13 currency pairs over a 19-month period. We examine the joint evolution of 1 month, 2 month, 3 month, 6 month and 1 year at-the-money (50 δ) options in all the currency pairs. We show that there exist three uncorrelated state variables (principal components) which account for the parallel movement, slope oscillation, and curvature of the term structure and which explain, on average, the movements of the termstructure of volatility to more than 95% in all cases. We test and construct an exponential ARCH, or E-ARCH, model for each state variable. One of the applications of this model is to produce confidence bands for the term structure of volatility. Journal: Applied Mathematical Finance Pages: 81-100 Issue: 2 Volume: 4 Year: 1997 Keywords: currency options, term structure of volatility, ARCH, E-ARCH, X-DOI: 10.1080/13504869700000001 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869700000001 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:2:p:81-100 Template-Type: ReDIF-Article 1.0 Author-Name: K. T. Au Author-X-Name-First: K. T. Author-X-Name-Last: Au Author-Name: A. B. Sim Author-X-Name-First: A. B. Author-X-Name-Last: Sim Author-Name: D. C. Thurston Author-X-Name-First: D. C. Author-X-Name-Last: Thurston Title: Markovian spot rate dynamics with stochastic volatility structures Abstract: Recent studies of bond pricing dynamics and stochastic term structure models have focused on Markovian spot rate processes with deterministic volatilities. In this paper we provide and extension to allow for stochastic volatility functions and investigate conditions under which the dynamics of the spot rate is a Markov process. Journal: Applied Mathematical Finance Pages: 101-108 Issue: 2 Volume: 4 Year: 1997 Keywords: Markovian, bond pricing, Heath, Jarrow, Morton, stochastic volatility, X-DOI: 10.1080/13504869700000002 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869700000002 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:2:p:101-108 Template-Type: ReDIF-Article 1.0 Author-Name: C. Atkinson Author-X-Name-First: C. Author-X-Name-Last: Atkinson Author-Name: B. Al-Ali Author-X-Name-First: B. Author-X-Name-Last: Al-Ali Title: On an investment-consumption model with transaction costs: an asymptotic analysis Abstract: In this paper we examine the Akian, Menaldi and Sulem (1996) model for the optimal management of a portfolio, when there are transaction costs which are equal to a fixed percentage of the amount transacted. We analyse this model in the realistic limit of small transaction costs. Although the full problem is a free boundary diffusion problem in as many dimensions as there are assets in the portfolio, we find explicit solutions for the optimal trading policy in this limit. This makes the solution for a realistically large number of assets a practical possibility. Journal: Applied Mathematical Finance Pages: 109-133 Issue: 2 Volume: 4 Year: 1997 Keywords: portfolio management, investment-consumption model, transaction costs, X-DOI: 10.1080/13504869700000003 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869700000003 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:2:p:109-133 Template-Type: ReDIF-Article 1.0 Author-Name: Umberto Cherubini Author-X-Name-First: Umberto Author-X-Name-Last: Cherubini Title: Fuzzy measures and asset prices: accounting for information ambiguity Abstract: A recent stream of literature has suggested that many market imperfections or 'puzzles' can be easily explained once information ambiguity, or knightian uncertainty is taken into account. Here we propose a parametric representation of this concept by means of a special class of fuzzy measures, known as gλ-measures. The parameter λ may be considered an indicator of uncertainty. Starting with a distribution, a value λ in (0, ∞) and a benchmark utility function we obtain a sub-additive expected utility, representing uncertainty aversion. A dual value λ* in (-1, 0) defining a super-additive expected utility is also recovered, while the benchmark expected utility is obtained for λ = λ* = 0. The two measures may be considered as lower and upper bounds of expected utility with respect to a set of probability measures, in the spirit of Gilboa-Schmeidler MMEU theory and of Dempster probability interval approach. The parametrization may be used to determine the effect of information ambiguity on asset prices in a very straightforward way. As examples, we determine the price of a corporate debt contract and a 'fuzzified' version of the Black and Scholes model. Journal: Applied Mathematical Finance Pages: 135-149 Issue: 3 Volume: 4 Year: 1997 Keywords: Knightian Uncertainty, Market Incompleteness, Non-additive Measures, Asset Pricing, X-DOI: 10.1080/135048697334773 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334773 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:3:p:135-149 Template-Type: ReDIF-Article 1.0 Author-Name: Marek Rutkowski Author-X-Name-First: Marek Author-X-Name-Last: Rutkowski Title: A note on the Flesaker-Hughston model of the term structure of interest rates Abstract: A term structure model proposed by Flesaker and Hughston (1996a,b) is analysed within the general framework of arbitrage-free term structure modelling. Basic valuation formulae for caps and swaptions are presented. Journal: Applied Mathematical Finance Pages: 151-163 Issue: 3 Volume: 4 Year: 1997 Keywords: Swaption, Term Structure Of Interest Rates, Zero-coupon Bond, X-DOI: 10.1080/135048697334782 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334782 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:3:p:151-163 Template-Type: ReDIF-Article 1.0 Author-Name: Emmanuel Acar Author-X-Name-First: Emmanuel Author-X-Name-Last: Acar Author-Name: Stephen Satchell Author-X-Name-First: Stephen Author-X-Name-Last: Satchell Title: A theoretical analysis of trading rules: an application to the moving average case with Markovian returns Abstract: A general framework for analysing trading rules is presented. We discuss different return concepts and different statistical processes for returns. We then concentrate on moving average trading rules and show, in the case of moving average models of length two, closed form expressions for the characteristic function of realized returns when the underlying return process follows a switching Markovian Gaussian process. An example is included which illustrates the technique. Journal: Applied Mathematical Finance Pages: 165-180 Issue: 3 Volume: 4 Year: 1997 Keywords: Moving Averages, Switching Markov Models, Trading Rules, X-DOI: 10.1080/135048697334791 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334791 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:3:p:165-180 Template-Type: ReDIF-Article 1.0 Author-Name: Ramaprasad Bhar Author-X-Name-First: Ramaprasad Author-X-Name-Last: Bhar Author-Name: Carl Chiarella Author-X-Name-First: Carl Author-X-Name-Last: Chiarella Title: Interest rate futures: estimation of volatility parameters in an arbitrage-free framework Abstract: Hedging interest rate exposures using interest rate futures contracts requires some knowledge of the volatility function of the interest rates. Use of historical data as well as interest rate options like caps and swaptions to estimate this volatility function have been proposed in the literature. In this paper the interest rate futures price is modelled within an arbitrage-free framework for a volatility function which includes a stochastic variable, the instantaneous spot interest rate. The resulting system is expressed in a state space form which is solved using an extended Kalman filter. The residual diagnostics indicate suitability of the model and the bootstrap resampling technique is used to obtain small sample properties of the parameters of the volatility function. Journal: Applied Mathematical Finance Pages: 181-199 Issue: 4 Volume: 4 Year: 1997 Keywords: Interest Rate Futures;Heath-jarrow-morton Model;Arbitrage-free;Kalman Filter;Bootstrap, X-DOI: 10.1080/135048697334737 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334737 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:4:p:181-199 Template-Type: ReDIF-Article 1.0 Author-Name: M. F. Omran Author-X-Name-First: M. F. Author-X-Name-Last: Omran Title: Moment condition failure in stock returns: UK evidence Abstract: We examine the issue of moments existence in the UK stock market. It is found that the second moment of stock returns is finite, and therefore, the infinite variance stable distribution is ruled out as a candidate for modelling stock returns. In contrast with the US evidence, we cannot rule out the possibility that the fourth moment is finite. Journal: Applied Mathematical Finance Pages: 201-206 Issue: 4 Volume: 4 Year: 1997 Keywords: Maximal Moment Exponents;Distributions Of Uk Stock Returns, X-DOI: 10.1080/135048697334746 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334746 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:4:p:201-206 Template-Type: ReDIF-Article 1.0 Author-Name: Antonella Basso Author-X-Name-First: Antonella Author-X-Name-Last: Basso Author-Name: Paolo Pianca Author-X-Name-First: Paolo Author-X-Name-Last: Pianca Title: On the relative efficiency of nth order and DARA stochastic dominance rules Abstract: It is known that third order stochastic dominance implies DARA dominance while no implications exist between higher orders and DARA dominance. A recent contribution points out that, with regard to the problem of determining lower and upper bounds for the price of a financial option, the DARA rule turns out to improve the stochastic dominance criteria of any order. In this paper the relative efficiency of the ordinary stochastic dominance and DARA criteria for alternatives with discrete distributions are compared, in order to see if the better performance of DARA criterion is also suitable for other practical applications. Moreover, the operational use of the stochastic dominance techniques for financial choices is deepened. Journal: Applied Mathematical Finance Pages: 207-222 Issue: 4 Volume: 4 Year: 1997 Keywords: Stochastic Dominance;Decreasing Absolute Risk Aversion;Financial Efficient Sets;Dynamic Programming, X-DOI: 10.1080/135048697334755 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334755 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:4:p:207-222 Template-Type: ReDIF-Article 1.0 Author-Name: Riccardo Rebonato Author-X-Name-First: Riccardo Author-X-Name-Last: Rebonato Title: A class of arbitrage-free log-normal-short-rate two-factor models Abstract: An arbitrage-free two-factor model is presented, which is driven by the short rate and the consol yield, and which ensures log-normal short rate and positive rates. The market price of an arbitrary (discrete) set of discount bonds is recovered by construction, and an arbitrary degree of correlation can be accommodated between the long yield and the spread. By virtue of its Markovian nature, the model can be mapped onto a recombining tree, and therefore readily lends itself to the evaluation of American and compound options, which are difficult to evaluate with non-Markovian log-normal forward-rate models such as HJM. Comparison with such a two-factor HJM model has given good agreement in so far as the pricing of one-look triggers is concerned. The calibration to caplets and European swaptions is discussed in detail. Journal: Applied Mathematical Finance Pages: 223-236 Issue: 4 Volume: 4 Year: 1997 Keywords: Interest-rate Option Models;Short Rate;Consol Yield;Markovian Models;Two-factor Models, X-DOI: 10.1080/135048697334764 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048697334764 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:4:y:1997:i:4:p:223-236 Template-Type: ReDIF-Article 1.0 Author-Name: Clifford Ball Author-X-Name-First: Clifford Author-X-Name-Last: Ball Author-Name: Antonio Roma Author-X-Name-First: Antonio Author-X-Name-Last: Roma Title: Detecting mean reversion within reflecting barriers: application to the European Exchange Rate Mechanism Abstract: This paper derives a statistical test, based on the first-order autocorrelation, to ascertain whether a stochastic process evolving within reflecting barriers is mean reverting. Under these conditions the standard unit root analysis does not apply. Since the presence of reflecting barriers per se will induce mean reverting behaviour, the detection of mean reversion inside the two boundaries requires that the effect of reflection be properly accounted for. This statistical procedure may be useful in a number of economic applications which involve an assesment on the dynamics of bounded variables: e.g. the estimation of the mean reversion of ratios in capital structure theory, market share analysis, or the empirical testing of target zones models for exchange rates. We exemplify the inappropriateness of standard unit root analysis in these situations using European Monetary System exchange rate data. Our methodology is helpful in deciding whether the mean reverting behaviour of these exchange rates is due solely to local behaviour at the barriers, or whether a more complex interpretation is warranted. We apply our test to the target zone model introduced by Krugman where the intervention bands are credible. We study bilateral exchange rates of currencies party to the European Monetary System during a period of sustained stability consistent with the credible band assumption. Our results are consistent with those obtained employing significantly more complex maximum likelihood procedures. Journal: Applied Mathematical Finance Pages: 1-15 Issue: 1 Volume: 5 Year: 1998 Keywords: C51;F33, X-DOI: 10.1080/135048698334709 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334709 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:1:p:1-15 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Yisong Tian Author-X-Name-First: Yisong Author-X-Name-Last: Tian Title: An explicit finite difference approach to the pricing of barrier options Abstract: A modified explicit finite difference approach to the pricing of barrier options is developed. To obtain accurate prices, the grid is constructed such that the barrier is located in a suitable position relative to horizontal layers of nodes on the grid. This means that the barrier passes through a horizontal layer of nodes for continuous-time barrier options and is located halfway between two horizontal layers of nodes for discrete-time barrier options. Both single and double barrier cases can be accommodated. The option price at each node on the grid may be obtained by implementing a standard trinomial tree procedure. As the initial asset price will generally not lie exactly on the grid, the current value of the option is obtained using a quadratic interpolation of the option prices at the three adjacent nodes. The approach is shown to be robust and to provide accurate option prices and hedge ratios (such as delta, gamma, and theta) regardless of whether or not the barrier is close to the initial asset price, and it works effectively for both continuous-time and discrete-time barrier options. This device of adjusting the grid so that the barrier and the asset price lie on the grid is well known in the numerical analysis area. Journal: Applied Mathematical Finance Pages: 17-43 Issue: 1 Volume: 5 Year: 1998 Keywords: Barrier Options;Finite Differences;Option Pricing, X-DOI: 10.1080/135048698334718 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334718 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:1:p:17-43 Template-Type: ReDIF-Article 1.0 Author-Name: K. Ronnie Sircar Author-X-Name-First: K. Ronnie Author-X-Name-Last: Sircar Author-Name: George Papanicolaou Author-X-Name-First: George Author-X-Name-Last: Papanicolaou Title: General Black-Scholes models accounting for increased market volatility from hedging strategies Abstract: Increases in market volatility of asset prices have been observed and analysed in recent years and their cause has generally been attributed to the popularity of portfolio insurance strategies for derivative securities. The basis of derivative pricing is the Black-Scholes model and its use is so extensive that it is likely to influence the market itself. In particular it has been suggested that this is a factor in the rise in volatilities. A class of pricing models is presented that accounts for the feedback effect from the Black-Scholes dynamic hedging strategies on the price of the asset, and from there back onto the price of the derivative. These models do predict increased implied volatilities with minimal assumptions beyond those of the Black-Scholes theory. They are characterized by a nonlinear partial differential equation that reduces to the Black-Scholes equation when the feedback is removed. We begin with a model economy consisting of two distinct groups of traders: reference traders who are the majority investing in the asset expecting gain, and programme traders who trade the asset following a Black-Scholes type dynamic hedging strategy, which is not known a priori, in order to insure against the risk of a derivative security. The interaction of these groups leads to a stochastic process for the price of the asset which depends on the hedging strategy of the programme traders. Then following a Black-Scholes argument, we derive nonlinear partial differential equations for the derivative price and the hedging strategy. Consistency with the traditional Black-Scholes model characterizes the class of feedback models that we analyse in detail. We study the nonlinear partial differential equation for the price of the derivative by perturbation methods when the programme traders are a small fraction of the economy, by numerical methods, which are easy to use and can be implemented efficiently, and by analytical methods. The results clearly support the observed increasing volatility phenomenon and provide a quantitative explanation for it. Journal: Applied Mathematical Finance Pages: 45-82 Issue: 1 Volume: 5 Year: 1998 Keywords: Black-scholes Model;Dynamic Hedging;Feedback Effects;Option Pricing;Volatility, X-DOI: 10.1080/135048698334727 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334727 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:1:p:45-82 Template-Type: ReDIF-Article 1.0 Author-Name: Raymond Ross Author-X-Name-First: Raymond Author-X-Name-Last: Ross Title: Good point methods for computing prices and sensitivities of multi-asset European style options Abstract: Using number-theoretic methods, we investigate low-discrepancy sequences and weighted-sum estimators which outperform standard low-discrepancy techniques for pricing multi-asset European options on up to 5 underlying factors. The sequences used are simpler to implement than most low-discrepancy sequences, and computation time is considerably faster. Journal: Applied Mathematical Finance Pages: 83-106 Issue: 2 Volume: 5 Year: 1998 Keywords: Low Discrepancy Sequences;Option Pricing;Numerical Integration, X-DOI: 10.1080/135048698334664 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334664 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:2:p:83-106 Template-Type: ReDIF-Article 1.0 Author-Name: Rachel Kuske Author-X-Name-First: Rachel Author-X-Name-Last: Kuske Author-Name: Joseph Keller Author-X-Name-First: Joseph Author-X-Name-Last: Keller Title: Optimal exercise boundary for an American put option Abstract: The optimal exercise boundary near the expiration time is determined for an American put option. It is obtained by using Green's theorem to convert the boundary value problem for the price of the option into an integral equation for the optimal exercise boundary. This integral equation is solved asymptotically for small values of the time to expiration. The leading term in the asymptotic solution is the result of Barles et al. An asymptotic solution for the option price is obtained also. Journal: Applied Mathematical Finance Pages: 107-116 Issue: 2 Volume: 5 Year: 1998 Keywords: Put Option;Exercise Boundary;American Option;Free Boundary, X-DOI: 10.1080/135048698334673 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334673 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:2:p:107-116 Template-Type: ReDIF-Article 1.0 Author-Name: Moshe Arye Milevsky Author-X-Name-First: Moshe Arye Author-X-Name-Last: Milevsky Author-Name: Steven Posner Author-X-Name-First: Steven Author-X-Name-Last: Posner Title: A theoretical investigation of randomized asset allocation strategies Abstract: The traditional paradigm of Markowitz-Sharpe diversification stipulates the partition of wealth among the universe of all available investments. For an investor with constant relative risk aversion (CRRA) preferences, the optimal constantly rebalanced allocation is invariant in the dimension of time. In this paper the implications of reshuffling an investor's entire wealth among asset classes according to the stochastic outcome of a Bernoulli (zero or one) random variable is examined. In other words, at any point in time the investor is in only one, albeit random, asset class. The Bernoulli random variables can be constructed so that the investor obtains the exact same level of expected wealth as the 'constantly rebalanced' strategy. Over time, by the law of large numbers, this portfolio becomes randomly diversified. Technically, the probability density function (pdf) of the 'constantly rebalanced' strategy in continuous time is derived using a new proof that does not require Ito's lemma. The pdf of the randomized Bernoulli strategy (RBS) in continuous time is then derived and contrasted with the pdf arising from 'constantly rebalanced' diversification. It is shown that the two pdfs have the same probabilistic functioned form, namely, the log normal distribution, albeit with different parameter values. Although both strategies share the same expected value, the variance and skewness of the Bernoulli strategy is greater than its continuously rebalanced counterpart. Investors with mean-variance or CRRA utility will avoid randomization. However, those with a partially convex utility function or a preference for skewness are likely to select this strategy. As a by-product, an analytic expression is provided for the market timing penalty of a strategic asset allocator whose decisions are based on pure noise. Also provided is an application to the pricing of a second generation exotic option where the payoff function depends on the stochastic combination of two underlying assets. Journal: Applied Mathematical Finance Pages: 117-130 Issue: 2 Volume: 5 Year: 1998 Keywords: Asset Allocation Utility;Randomization;Exotic Options, X-DOI: 10.1080/135048698334682 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334682 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:2:p:117-130 Template-Type: ReDIF-Article 1.0 Author-Name: Riccardo Rebonato Author-X-Name-First: Riccardo Author-X-Name-Last: Rebonato Author-Name: Ian Cooper Author-X-Name-First: Ian Author-X-Name-Last: Cooper Title: Coupling backward induction with Monte Carlo simulations: a fast Fourier transform (FFT) approach Abstract: This note presents a simple, robust and computationally efficient way to calculate expectations of arbitrary future payoffs within the context of a Monte Carlo forward-induction methodology. The technique complements existing approximation techniques: while virtually all existing approximation methodologies remain approximate irrespective of the computational effort, the technique presented here has the desirable feature of being asymptotically 'correct', as long as 'weak' convergence in distribution is required. The proposed technique is applicable for the evaluation of both American options and compound options. The paper uses the fast Fourier transform (FFT) to evaluate along a simulated path the expectation of future pay-offs for an American option, conditional on the optimal exercise strategy. This technique can recover in a single pass the value function for a particular option across a wide range of values of the state variable and all future dates up to the maturity of the option. An example is given for a single state variable following a Markov process. The technique is shown to be fast and accurate in recovering both values and hedge ratios. The extension to several variables is straightforward. Journal: Applied Mathematical Finance Pages: 131-141 Issue: 2 Volume: 5 Year: 1998 Keywords: Option Valuation;Monte Carlo;Fourier Transform;Simulation, X-DOI: 10.1080/135048698334691 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334691 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:2:p:131-141 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Ericsson Author-X-Name-First: Jan Author-X-Name-Last: Ericsson Author-Name: Joel Reneby Author-X-Name-First: Joel Author-X-Name-Last: Reneby Title: A framework for valuing corporate securities Abstract: We suggest a methodology for valuing corporate securities that allows the straightforward derivation of closed form solutions for complex scenarios. The tractability of the framework stems from its modularity-we provide a number of intuitive building blocks that are sufficient for valuation in typical situations. A further advantage of our approach is that it makes economic interpretation far easier than what is typically possible with other approaches, such as solving systems of partial differential equations. As examples we consider a corporate coupon bond with discrete payments, and debt subject to strategic debt service. Journal: Applied Mathematical Finance Pages: 143-163 Issue: 3-4 Volume: 5 Year: 1998 Keywords: Option Pricing, Barrier Options, Corporate Debt, Credit Risk, X-DOI: 10.1080/135048698334619 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334619 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:3-4:p:143-163 Template-Type: ReDIF-Article 1.0 Author-Name: Grazyna Wolczynska Author-X-Name-First: Grazyna Author-X-Name-Last: Wolczynska Title: Option pricing in incomplete discrete markets Abstract: Various methods of option pricing in discrete time models are discussed. The classical risk minimization method often results in negative prices and a natural modification is proposed. Another method of risk minimization using an inductive procedure as in the Cox-Ross-Rubinstein model is also proposed. The definition of the risk interpreted as the maximum of possible loss is discussed. Journal: Applied Mathematical Finance Pages: 165-179 Issue: 3-4 Volume: 5 Year: 1998 Keywords: Incomplete Markets, Derivative Securities, X-DOI: 10.1080/135048698334628 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334628 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:3-4:p:165-179 Template-Type: ReDIF-Article 1.0 Author-Name: G. Caginalp Author-X-Name-First: G. Author-X-Name-Last: Caginalp Author-Name: H. Laurent Author-X-Name-First: H. Author-X-Name-Last: Laurent Title: The predictive power of price patterns Abstract: Using two sets of data, including daily prices (open, close, high and low) of all S&P 500 stocks between 1992 and 1996, we perform a satistical test of the predictive capability of candlestick patterns. Out-of-sample tests indicate statistical significance at the level of 36 standard deviations from the null hypothesis, and indicate a profit of almost 1% during a two-day holding period. An essentially non-parametric test utilizes standard definitions of three-day candlestick patterns and removes conditions on magnitudes. The results provide evidence that traders are influenced by price behaviour. To the best of our knowledge, this is the first scientific test to provide strong evidence in favour of any trading rule or pattern on a large unrestricted scale. Journal: Applied Mathematical Finance Pages: 181-205 Issue: 3-4 Volume: 5 Year: 1998 Keywords: Candlestick Patterns, Statistical Price Prediction, Price Pattern, Technical Analysis, X-DOI: 10.1080/135048698334637 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334637 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:3-4:p:181-205 Template-Type: ReDIF-Article 1.0 Author-Name: Isabelle Bajeux-Besnainou Author-X-Name-First: Isabelle Author-X-Name-Last: Bajeux-Besnainou Author-Name: Roland Portait Author-X-Name-First: Roland Author-X-Name-Last: Portait Title: Pricing stock and bond derivatives with a multi-factor Gaussian model Abstract: The martingale approach to pricing contingent claims can be applied in a multiple state variable model. The idea is used to derive the prices of derivative securities (futures on stock and bond futures, options on stocks, bonds and futures) given a continuous time Gaussian multi-factor model of the returns of stocks and bonds. The bond market is similar to Langetieg's multi-factor model, which has closed-form solutions. This model is a generalization of Vasicek's model, where the term structure depends on state variables following correlated mean reverting processes. The stock market is affected by systematic and unsystematic risk. Journal: Applied Mathematical Finance Pages: 207-225 Issue: 3-4 Volume: 5 Year: 1998 Keywords: Derivative Securities, Multi-factor Model, Continuous-time, Pricing, X-DOI: 10.1080/135048698334646 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334646 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:3-4:p:207-225 Template-Type: ReDIF-Article 1.0 Author-Name: Farid Aitsahlia Author-X-Name-First: Farid Author-X-Name-Last: Aitsahlia Author-Name: Tzeung Le Lai Author-X-Name-First: Tzeung Le Author-X-Name-Last: Lai Title: Random walk duality and the valuation of discrete lookback options Abstract: Use is made of the duality property of random walks to develop a numerical method for the valuation of discrete-time lookback options. This method leads to a recursive numerical integration procedure which is fast, accurate and easy to implement. Journal: Applied Mathematical Finance Pages: 227-240 Issue: 3-4 Volume: 5 Year: 1998 Keywords: Exotic Options, Lookback Options, Recursive Numerical Integration, Random Walk Duality, X-DOI: 10.1080/135048698334655 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048698334655 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:5:y:1998:i:3-4:p:227-240 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Avellaneda Author-X-Name-First: Marco Author-X-Name-Last: Avellaneda Author-Name: Robert Buff Author-X-Name-First: Robert Author-X-Name-Last: Buff Title: Combinatorial implications of nonlinear uncertain volatility models: the case of barrier options Abstract: Extensions to the Black-Scholes model have been suggested recently that permit one to calculate worst-case prices for a portfolio of vanilla options or for exotic options when no a priori distribution for the forward volatility is known. The Uncertain Volatility Model (UVM) by Avellaneda and Paras finds a one-sided worstcase volatility scenario for the buy resp. sell side within a specified volatility range. A key feature of this approach is the possibility of hedging with options: risk cancellation leads to super resp. sub-additive portfolio values. This nonlinear behaviour causes the combinatorial complexity of the pricing problem to increase significantly in the case of barrier options. In the paper, it is shown that for a portfolio P of n barrier options and any number of vanilla options, the number of PDEs that have to be solved in a hierarchical manner in order to solve the UVM problem for P is bounded by O (n2). A numerically stable implementation is described and numerical results are given. Journal: Applied Mathematical Finance Pages: 1-18 Issue: 1 Volume: 6 Year: 1999 Keywords: Uncertain Volatility Model, Barrier Options, Pricing, X-DOI: 10.1080/135048699334582 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334582 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:1:p:1-18 Template-Type: ReDIF-Article 1.0 Author-Name: William Morokoff Author-X-Name-First: William Author-X-Name-Last: Morokoff Title: Numerical integration of mean reverting stochastic systems with applications to interest rate term structure simulation Abstract: A proof of convergence is presented for a simplified numerical integration method for solving systems of correlated stochastic differential equations describing mean reverting geometric Brownian motion. Such systems arise in modelling the time evolution of interest rate term structures. For time discretization of size Δt, the method leads to global error in time of O (Δt2) and no error accumulation. The result is shown to extend to the case when principal components analysis is used to reduce the number of underlying stochastic factors. Journal: Applied Mathematical Finance Pages: 19-28 Issue: 1 Volume: 6 Year: 1999 Keywords: Numerical Integration, Stochastic Differential Systems, Mean Reversion, Term Structure, Simulation, Value-at-risk, X-DOI: 10.1080/135048699334591 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334591 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:1:p:19-28 Template-Type: ReDIF-Article 1.0 Author-Name: Marek Rutkowski Author-X-Name-First: Marek Author-X-Name-Last: Rutkowski Title: Models of forward Libor and swap rates Abstract: The backward induction approach is systematically used to produce various models of forward market rates. These include the lognormal model of forward Libor rates examined by Miltersen et al. and Brace et al., as well as the lognormal model of (fixed-maturity) forward swap rates, which was proposed by Jamshidian. The valuation formulae for European caps and swaptions are given. In the last section, the Eurodollar futures contracts and options are examined within the framework of the lognormal model of forward Libor rates. Journal: Applied Mathematical Finance Pages: 29-60 Issue: 1 Volume: 6 Year: 1999 Keywords: Zero-coupon Bond, Libor Rate, Swap Rate, Swaption, Eurodollar Futures, X-DOI: 10.1080/135048699334609 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334609 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:1:p:29-60 Template-Type: ReDIF-Article 1.0 Author-Name: Graziella Pacelli Author-X-Name-First: Graziella Author-X-Name-Last: Pacelli Author-Name: Maria Cristina Recchioni Author-X-Name-First: Maria Cristina Author-X-Name-Last: Recchioni Author-Name: Francesco Zirilli Author-X-Name-First: Francesco Author-X-Name-Last: Zirilli Title: A hybrid method for pricing European options based on multiple assets with transaction costs Abstract: The problem of pricing European options based on multiple assets with transaction costs is considered. These options include, for example, quality options and options on the minimum of two or more risky assets. The value of these options is the solution of a nonlinear parabolic partial differential equation subject to a final condition given by the payoff function associated with the option. A computationally efficient method to solve this final-value problem is proposed. This method is based on an asymptotic expansion of the required solution with respect to the parameters related to the transaction costs followed by the numerical solution of the linear partial differential equations obtained at each order in perturbation theory. The numerical solution of these linear problems involves an implicit finite-difference scheme for the parabolic equation and the use of the fast Fourier sine transform to solve the resulting elliptic problems. Numerical results obtained on test problems with the method proposed here are shown and discussed. Journal: Applied Mathematical Finance Pages: 61-85 Issue: 2 Volume: 6 Year: 1999 Keywords: Options Pricing, Multiple Assets, Transaction Costs, Partial Differential Equations, Asymptotic, Expansion, Numerical Method, X-DOI: 10.1080/135048699334555 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334555 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:2:p:61-85 Template-Type: ReDIF-Article 1.0 Author-Name: P. A. Forsyth Author-X-Name-First: P. A. Author-X-Name-Last: Forsyth Author-Name: K. R. Vetzal Author-X-Name-First: K. R. Author-X-Name-Last: Vetzal Author-Name: R. Zvan Author-X-Name-First: R. Author-X-Name-Last: Zvan Title: A finite element approach to the pricing of discrete lookbacks with stochastic volatility Abstract: Finite element methods are described for valuing lookback options under stochastic volatility. Particular attention is paid to the method for handling the boundary equations. For some boundaries, the equations reduce to first-order hyperbolic equations which must be discretized to ensure that outgoing waves are correctly modelled. Some example computations show that for certain choices of parameters, the option price computed for a lookback under stochastic volatility can differ from the price under the usual constant volatility assumption by as much as 35% (i.e. $7.30 compared with $5.45 for an at-the-money put), even though the models are calibrated so as to produce exactly the same price for an at-the-money vanilla European option with the same time remaining until expiry. Journal: Applied Mathematical Finance Pages: 87-106 Issue: 2 Volume: 6 Year: 1999 Keywords: Finite Element, Lookback, Stochastic Volatility, X-DOI: 10.1080/135048699334564 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334564 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:2:p:87-106 Template-Type: ReDIF-Article 1.0 Author-Name: K. Ronnie Sircar Author-X-Name-First: K. Ronnie Author-X-Name-Last: Sircar Author-Name: George Papanicolaou Author-X-Name-First: George Author-X-Name-Last: Papanicolaou Title: Stochastic volatility, smile & asymptotics Abstract: We consider the pricing and hedging problem for options on stocks whose volatility is a random process. Traditional approaches, such as that of Hull and White, have been successful in accounting for the much observed smile curve, and the success of a large class of such models in this respect is guaranteed by a theorem of Renault and Touzi, for which we present a simplified proof. Motivated by the robustness of the smile effect to specific modelling of the unobserved volatility process, we introduce a methodology that does not depend on a particular stochastic volatility model. We start with the Black-Scholes pricing PDE with a random volatility coefficient. We identify and exploit distinct time scales of fluctuation for the stock price and volatility processes yielding an asymptotic approximation that is a Black-Scholes type price or hedging ratio plus a Gaussian random variable quantifying the risk from the uncertainty in the volatility. These lead us to translate volatility risk into pricing and hedging bands for the derivative securities, without needing to estimate the market's value of risk or to specify a parametric model for the volatility process. For some special cases, we can give explicit formulas. We outline how this method can be used to save on the cost of hedging in a random volatility environment, and run simulations demonstrating its effectiveness. The theory needs estimation of a few statistics of the volatility process, and we run experiments to obtain approximations to these from simulated stock price and smile curve data. Journal: Applied Mathematical Finance Pages: 107-145 Issue: 2 Volume: 6 Year: 1999 Keywords: Option Pricing, Volatility, Stochastic Volatility Models, Hedging, Smile, Curve, X-DOI: 10.1080/135048699334573 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334573 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:2:p:107-145 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Hagan Author-X-Name-First: Patrick Author-X-Name-Last: Hagan Author-Name: Diana Woodward Author-X-Name-First: Diana Author-X-Name-Last: Woodward Title: Equivalent Black volatilities Abstract: We consider European calls and puts on an asset whose forward price F(t) obeys dF(t)=α(t)A(F)dW(t,) under the forward measure. By using singular perturbation techniques, we obtain explicit algebraic formulas for the implied volatility σB in terms of today's forward price F0 ≡ F(0), the strike K of the option, and the time to expiry tex. The price of any call or put can then be calculated simply by substituting this implied volatility into Black's formula. For example, for a power law (constant elasticity of variance) model dF(t)=aFβdW(t) we obtain σB = a/faυ1-β {1 + (1-β)(2+β)/24 (F0 - K/faυ)2 + (1 - β)2/24 a2tex/faυ2-2β +…} where faυ = ½(F0 + K). Our formula for the implied volatility is not exact. However, we show that the error is insignificant, rarely approaching 1/1000 of the time value of the option. We also present more accurate (albeit more complicated) formulas which can be used for the implied volatility. Journal: Applied Mathematical Finance Pages: 147-157 Issue: 3 Volume: 6 Year: 1999 Keywords: Skews, Smiles, Implied Volatility, Black-scholes, Options, X-DOI: 10.1080/135048699334500 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334500 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:147-157 Template-Type: ReDIF-Article 1.0 Author-Name: Silvia Florio Author-X-Name-First: Silvia Author-X-Name-Last: Florio Author-Name: Wolfgang Runggaldier Author-X-Name-First: Wolfgang Author-X-Name-Last: Runggaldier Title: On hedging in finite security markets Abstract: A market is considered where trading can take place only at discrete time points, the trading frequency cannot grow without bound, and the number of states of nature is finite. The main objectives of the paper are to show that the market can be completed also with highly correlated risky assets, and to describe an efficient algorithm to compute a self-financing hedging strategy. The algorithm consists off-line of a backwards recursion and on-line of the solution, in each period, of a system of linear equations; it is a consequence of a proof where, using a well-known mathematical property, it is shown that uniqueness of the martingale measure implies completeness also in our setting. The significance of 'multistate' models versus the familiar binomial model is discussed and it is shown how the evolution of prices of the (correlated) risky assets can be chosen so that a given probability measure is already the unique equivalent martingale measure. Journal: Applied Mathematical Finance Pages: 159-176 Issue: 3 Volume: 6 Year: 1999 Keywords: Finite Security Markets, Discrete Time Trading, Equivalent Martingale Measures, Market Completion, Self-financing Hedging Strategies, X-DOI: 10.1080/135048699334519 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334519 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:159-176 Template-Type: ReDIF-Article 1.0 Author-Name: Nigel Clarke Author-X-Name-First: Nigel Author-X-Name-Last: Clarke Author-Name: Kevin Parrott Author-X-Name-First: Kevin Author-X-Name-Last: Parrott Title: Multigrid for American option pricing with stochastic volatility Abstract: The paper describes an implicit finite difference approach to the pricing of American options on assets with a stochastic volatility. A multigrid procedure is described for the fast iterative solution of the discrete linear complementarity problems that result. The accuracy and performance of this approach is improved considerably by a strike-price related analytic transformation of asset prices and adaptive time-stepping. Journal: Applied Mathematical Finance Pages: 177-195 Issue: 3 Volume: 6 Year: 1999 Keywords: American Option Pricing, Stochastic Volatility, Finite Difference Method, Multigrid, Strike-price Related Transformation, Adaptive Time-stepping, X-DOI: 10.1080/135048699334528 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334528 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:177-195 Template-Type: ReDIF-Article 1.0 Author-Name: Hyungsok Ahn Author-X-Name-First: Hyungsok Author-X-Name-Last: Ahn Author-Name: Adviti Muni Author-X-Name-First: Adviti Author-X-Name-Last: Muni Author-Name: Glen Swindle Author-X-Name-First: Glen Author-X-Name-Last: Swindle Title: Optimal hedging strategies for misspecified asset price models Abstract: The Black-Scholes option pricing methodology requires that the model for the price of the underlying asset be completely specified. Often the underlying price is taken to be a geometric Brownian motion with a constant, known volatility. In practice one does not know precise values of parameters such as the volatility, and estimates from historical prices or implied volatilities must be used instead. In this paper optimal hedging strategies are constructed when the volatility of the asset price is misspecified. Optimality refers to maximizing the utility of the investor in a worst-case volatility scenario. Journal: Applied Mathematical Finance Pages: 197-208 Issue: 3 Volume: 6 Year: 1999 Keywords: Incomplete Markets, Option Hedging Strategies, h Control, Stochastic Differential Games, X-DOI: 10.1080/135048699334537 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334537 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:197-208 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Philippe Bouchaud Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Bouchaud Author-Name: Nicolas Sagna Author-X-Name-First: Nicolas Author-X-Name-Last: Sagna Author-Name: Rama Cont Author-X-Name-First: Rama Author-X-Name-Last: Cont Author-Name: Nicole El-Karoui Author-X-Name-First: Nicole Author-X-Name-Last: El-Karoui Author-Name: Marc Potters Author-X-Name-First: Marc Author-X-Name-Last: Potters Title: Phenomenology of the interest rate curve Abstract: The paper contains a phenomenological description of the whole US forward rate curve (FRC), based on data in the period 1990-1996. It is found that the average deviation of the FRC from the spot rate grows as the square-root of the maturity, with a prefactor which is comparable to the spot rate volatility. This suggests that forward rate market prices include a risk premium, comparable to the probable changes of the spot rate between now and maturity, which can be understood as a 'Value-at-Risk' type of pricing. The instantaneous FRC, however, departs from a simple square-root law. The deformation is maximum around one year, and reflects the market anticipation of a local trend on the spot rate. This anticipated trend is shown to be calibrated on the past behaviour of the spot itself. It is shown that this is consistent with the volatility 'hump' around one year found by several authors (which is confirmed). Finally, the number of independent components needed to interpret most of the FRC fluctuations is found to be small. This is rationalized by showing that the dynamical evolution of the FRC contains a stabilizing second derivative (line tension) term, which tends to suppress short-scale distortions of the FRC. This shape-dependent term could lead to arbitrage. However, this arbitrage cannot be implemented in practice because of transaction costs. It is suggested that the presence of transaction costs (or other market 'imperfections') is crucial for model building, for a much wider class of models becomes eligible to represent reality.1 Journal: Applied Mathematical Finance Pages: 209-232 Issue: 3 Volume: 6 Year: 1999 Keywords: Forward Rate Curve, Spot Rate, Risk Premium, 'value-at-risk' Pricing, Volatility Hump, Deformation, X-DOI: 10.1080/135048699334546 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048699334546 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:3:p:209-232 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Hagan Author-X-Name-First: Patrick Author-X-Name-Last: Hagan Author-Name: Diana Woodward Author-X-Name-First: Diana Author-X-Name-Last: Woodward Title: Markov interest rate models Abstract: A general procedure for creating Markovian interest rate models is presented. The models created by this procedure automatically fit within the HJM framework and fit the initial term structure exactly. Therefore they are arbitrage free. Because the models created by this procedure have only one state variable per factor, twoand even three-factor models can be computed efficiently, without resorting to Monte Carlo techniques. This computational efficiency makes calibration of the new models to market prices straightforward. Extended Hull- White, extended CIR, Black-Karasinski, Jamshidian's Brownian path independent models, and Flesaker and Hughston's rational log normal models are one-state variable models which fit naturally within this theoretical framework. The 'separable' n-factor models of Cheyette and Li, Ritchken, and Sankarasubramanian - which require n(n + 3)/2 state variables - are degenerate members of the new class of models with n(n + 3)/2 factors. The procedure is used to create a new class of one-factor models, the 'β-η models.' These models can match the implied volatility smiles of swaptions and caplets, and thus enable one to eliminate smile error. The β-η models are also exactly solvable in that their transition densities can be written explicitly. For these models accurate - but not exact - formulas are presented for caplet and swaption prices, and it is indicated how these closed form expressions can be used to efficiently calibrate the models to market prices. Journal: Applied Mathematical Finance Pages: 233-260 Issue: 4 Volume: 6 Year: 1999 X-DOI: 10.1080/13504869950079275 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869950079275 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:4:p:233-260 Template-Type: ReDIF-Article 1.0 Author-Name: Lilly Choong Author-X-Name-First: Lilly Author-X-Name-Last: Choong Author-Name: George McKenzie Author-X-Name-First: George Author-X-Name-Last: McKenzie Title: The pricing of risky coupon bonds Abstract: It is shown that bond valuation without due consideration to debt-servicing arrangements can lead to a misspecification of default risks and hence in the credit rating attached to the bond. The general conclusion is that default probabilities depend not only upon a firm's leverage and the volatitily of its underlying asset returns but also on how its debt is funded. Unfortunately, there is no one single exposition in the literature which deals with this problem. The paper compares, in a systematic way, the structure of alternative debt-servicing arrangements and sinking fund provisions, first from a theoretical perspective and then through the use of numerical simulations. The existing theoretical literature takes one of two approaches: first, where the funding of coupons takes place through the issue of new equity, and second, where the coupons are funded through deductions from the assets of the issuer. Both involve different stochastic processes and valuation procedures. These two cases are each examined under two different scenarios: (i) payment of the coupon at each servicing date with face value repaid at maturity; and (ii) a sinking fund involving mandatory redemption where firms retire a proportion of the debt each period at face value in addition to making coupon payments on the outstanding debt. Each of these four scenarios has different implications for default risk. Journal: Applied Mathematical Finance Pages: 261-273 Issue: 4 Volume: 6 Year: 1999 Keywords: Coupon Bonds Credit Risk Credit Ratings, X-DOI: 10.1080/13504869950079284 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869950079284 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:4:p:261-273 Template-Type: ReDIF-Article 1.0 Author-Name: Hyungsok Ahn Author-X-Name-First: Hyungsok Author-X-Name-Last: Ahn Author-Name: Antony Penaud Author-X-Name-First: Antony Author-X-Name-Last: Penaud Author-Name: Paul Wilmott Author-X-Name-First: Paul Author-X-Name-Last: Wilmott Title: Various passport options and their valuation Abstract: The passport option is a call option on the balance of a trading account. The option holder retains the gain from trading, while the writer is liable for the loss. Multi-asset passport options and passport options with discrete constraints are studied. For the first ones the pricing equations are Hamilton-Jacobi-Bellman equations. For those with discrete constraints, a linear complementary problem must be solved in order to price the option. The gain by selling passport options to utility maximizing investors and to investors who guess the market a certain percentage of the time is also examined. Journal: Applied Mathematical Finance Pages: 275-292 Issue: 4 Volume: 6 Year: 1999 Keywords: Passport Option Trading Account Hamilton-JACOBI-BELLMAN Equation Option Pricing, X-DOI: 10.1080/13504869950079293 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869950079293 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:4:p:275-292 Template-Type: ReDIF-Article 1.0 Author-Name: Anna Rita Bacinello Author-X-Name-First: Anna Rita Author-X-Name-Last: Bacinello Author-Name: Fulvio Ortu Author-X-Name-First: Fulvio Author-X-Name-Last: Ortu Title: Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates Abstract: The paper tackles the problem of pricing, under interest-rate risk, a default-free sinking-fund bond which allows its issuer to recurrently retire part of the issue by (a) a lottery call at par, or (b) an open market repurchase. By directly modelling zero-coupon bonds as diffusions driven by a single-dimensional Brownian motion, a pricing formula is supplied for the sinking-fund bond based on a backward induction procedure which exploits, at each step, the martingale approach to the valuation of contingent-claims. With more than one sinking-fund date, however, the pricing formula is not in closed form, not even for simple parametrizations of the process for zerocoupon bonds, so that a numerical approach is needed. Since the computational complexity increases exponentially with the number of sinking-fund dates, arbitrage-based lower and upper bounds are provided for the sinking-fund bond price. The computation of these bounds is almost effortless when zero-coupon bonds are as described by Cox, Ingersoll and Ross. Numerical comparisons between the price of the sinking-fund bond obtained via Monte Carlo simulation and these lower and upper bounds are illustrated for different choices of parameters. Journal: Applied Mathematical Finance Pages: 293-312 Issue: 4 Volume: 6 Year: 1999 Keywords: Sinking-FUND Bonds Multiple Sinking-FUND Dates Interest Rate Risk Martingale Approach Cir Model Monte Carlo Simulation, X-DOI: 10.1080/13504869950079301 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504869950079301 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:6:y:1999:i:4:p:293-312 Template-Type: ReDIF-Article 1.0 Author-Name: Leif Andersen Author-X-Name-First: Leif Author-X-Name-Last: Andersen Author-Name: Jesper Andreasen Author-X-Name-First: Jesper Author-X-Name-Last: Andreasen Title: Volatility skews and extensions of the Libor market model Abstract: The paper considers extensions of the Libor market model to markets with volatility skews in observable option prices. The family of forward rate processes is expanded to include diffusions with non-linear forward rate dependence, and efficient techniques for calibration to quoted prices of caps and swaptions are discussed. Special emphasis is put on generalized CEV processes for which closed-form expressions for cap and swaption prices are derived. Modifications of the CEV process which exhibit more appealing growth and boundary characteristics are also discussed. The proposed models are investigated numerically through Crank-Nicholson finite difference schemes and Monte Carlo simulations. Journal: Applied Mathematical Finance Pages: 1-32 Issue: 1 Volume: 7 Year: 2000 Keywords: Libor Market Model Volatility Skews Observable Option Prices Cev Processes Crank-NICHOLSON Schemes Monte Carlo Simulation, X-DOI: 10.1080/135048600450275 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048600450275 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:1:p:1-32 Template-Type: ReDIF-Article 1.0 Author-Name: D. M. Pooley Author-X-Name-First: D. M. Author-X-Name-Last: Pooley Author-Name: P. A. Forsyth Author-X-Name-First: P. A. Author-X-Name-Last: Forsyth Author-Name: K. R. Vetzal Author-X-Name-First: K. R. Author-X-Name-Last: Vetzal Author-Name: R. B. Simpson Author-X-Name-First: R. B. Author-X-Name-Last: Simpson Title: Unstructured meshing for two asset barrier options Abstract: Discretely observed barriers introduce discontinuities in the solution of two asset option pricing partial differential equations (PDEs) at barrier observation dates. Consequently, an accurate solution of the pricing PDE requires a fine mesh spacing near the barriers. Non-rectangular barriers pose difficulties for finite difference methods using structured meshes. It is shown that the finite element method (FEM) with standard unstructured meshing techniques can lead to significant efficiency gains over structured meshes with a comparable number of vertices. The greater accuracy achieved with unstructured meshes is shown to more than compensate for a greater solve time due to an increase in sparse matrix condition number. Results are presented for a variety of barrier shapes, including rectangles, ellipses, and rotations of these shapes. It is claimed that ellipses best represent constant (risk neutral) probability regions of underlying asset price-point movement, and are thus natural two-dimensional barrier shapes. Journal: Applied Mathematical Finance Pages: 33-60 Issue: 1 Volume: 7 Year: 2000 Keywords: Finite Element Unstructured Meshing Barrier Options, X-DOI: 10.1080/135048600450284 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048600450284 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:1:p:33-60 Template-Type: ReDIF-Article 1.0 Author-Name: Junhwa Ban Author-X-Name-First: Junhwa Author-X-Name-Last: Ban Author-Name: Hyeong In Choi Author-X-Name-First: Hyeong In Author-X-Name-Last: Choi Author-Name: Hyejin Ku Author-X-Name-First: Hyejin Author-X-Name-Last: Ku Title: Valuation of European options in the market with daily price limit Abstract: A valuation problem of the European style contingent claim in the market with daily price movement limit is studied. Unlike the one leading to the well known Black-Scholes formula, this problem depicts considerable conceptual difficulty and anomaly created by the presence of various arbitrage opportunities inherently built in the model due to the daily price movement limit. The presence of arbitrage makes it go against the grain of the well established arbitrage pricing theory. In this paper, how these complications arise are discussed and then a valuation approach devised, which is called the 'vanishing transaction cost technique,' of getting around the difficulty. Journal: Applied Mathematical Finance Pages: 61-74 Issue: 1 Volume: 7 Year: 2000 Keywords: Geometric Brownian Motion With Boundary Slowly Reflecting Boundary Arbitrage Black-SCHOLES Formula Vanishing Transaction Cost Technique, X-DOI: 10.1080/135048600450293 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048600450293 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:1:p:61-74 Template-Type: ReDIF-Article 1.0 Author-Name: Hans-Peter Bermin Author-X-Name-First: Hans-Peter Author-X-Name-Last: Bermin Title: Hedging lookback and partial lookback options using Malliavin calculus Abstract: The paper considers a Black and Scholes economy with constant coefficients. A contingent claim is said to be simple if the payoff at maturity is a function of the value of the underlying security at maturity. To replicate a simple contingent claim one uses so called delta-hedging, and the well-known strategy is derived from Ito calculus and the theory of partial differentiable equations. However, hedging path-dependent options require other tools since the price processes, in general, no longer have smooth stochastic differentials. It is shown how Malliavin calculus can be used to derive the hedging strategy for any kind of path-dependent options, and in particular for lookback and partial lookback options. Journal: Applied Mathematical Finance Pages: 75-100 Issue: 2 Volume: 7 Year: 2000 Keywords: Contingent Claims Hedging Lookback Options Malliavin Calculus, X-DOI: 10.1080/13504860010014052 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860010014052 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:2:p:75-100 Template-Type: ReDIF-Article 1.0 Author-Name: C. Douglas Howard Author-X-Name-First: C. Douglas Author-X-Name-Last: Howard Title: Obtaining distributional information from valuation lattices Abstract: Efficient algorithms for obtaining information about the total return distribution of securities from valuation lattices are described. This information, including variances and covariances between securities, is useful when constructing hedging transactions that achieve specific objectives. Journal: Applied Mathematical Finance Pages: 101-114 Issue: 2 Volume: 7 Year: 2000 Keywords: Algorithm Return Distribution Of Securities Valuation Lattices Variance Covariance, X-DOI: 10.1080/13504860010013035 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860010013035 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:2:p:101-114 Template-Type: ReDIF-Article 1.0 Author-Name: Francisca Richter Author-X-Name-First: Francisca Author-X-Name-Last: Richter Author-Name: B. Wade Brorsen Author-X-Name-First: B. Wade Author-X-Name-Last: Brorsen Title: Estimating fees for managed futures: a continuous-time model with a knockout feature Abstract: Past research regarding incentive fees based on high-water marks has developed models for the specific characteristics of hedge funds. These theoretical models have used either discrete time or a Black-Scholes type differential equation. However, for managed futures, high-water marks are measured more frequently than for hedge funds, so a continuous-time model for managed futures may be appropriate. A knockout feature is added to a continuous model, which is something unique to managed futures although it could also have some relevance to hedge funds. The procedures allow one to derive the distribution function for the fund's survival time, which has not been derived in past research. The distribution of the maximum until ruin is derived as well, and used to provide an estimate of expected incentive fees. An estimate of the expected fixed fee is also obtained. The model shows that the expected incentive fee would be maximized if all funds were invested in margins, but for total fees to be maximized in the presence of a knockout feature, less than half of the funds should be invested. This is precisely what fund managers do. This result suggests that designing a fund with incentive fees only may cause fund managers to adopt the highest leverage, and thus, highest risk possible. Journal: Applied Mathematical Finance Pages: 115-125 Issue: 2 Volume: 7 Year: 2000 Keywords: Hedge Funds Managed Futures Incentive Fee High-WATER Marks Ruin, X-DOI: 10.1080/13504860010011163 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860010011163 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:2:p:115-125 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Satchell Author-X-Name-First: Stephen Author-X-Name-Last: Satchell Author-Name: David Damant Author-X-Name-First: David Author-X-Name-Last: Damant Author-Name: Soosung Hwang Author-X-Name-First: Soosung Author-X-Name-Last: Hwang Title: Exponential risk measure with application to UK asset allocation Abstract: In the paper the exponential risk measure of Damant and Satchell is used to formulate an investor's utility function and the properties of this function are investigated. The utility function is calibrated for a typical UK investor who would hold different proportions of equity. It is found that, for plausible parameter values, a typical UK investor will hold more equity under the assumption of non-normality of return if his utility function has the above formulation and not the standard mean-variance utility function. Furthermore, our utility function is consistent with positive skewness affection and kurtosis aversion. Some aggregate estimates of risk parameters are calculated for the typical UK investor. These do not seem well determined, raising issues of the roles of aggregation and wealth in this model. Journal: Applied Mathematical Finance Pages: 127-152 Issue: 2 Volume: 7 Year: 2000 Keywords: Exponential Risk Measure Utility Function Skewness Kurtosis Capm Downside Risk Asset Allocation, X-DOI: 10.1080/13504860010014502 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860010014502 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:2:p:127-152 Template-Type: ReDIF-Article 1.0 Author-Name: Shinichi Aihara Author-X-Name-First: Shinichi Author-X-Name-Last: Aihara Title: Estimation of stochastic volatility in the Hull-White model Abstract: Estimation of the stochastic volatility in the Hull-White framework is considered. Stock price is taken as the observation and the estimation problem is posed for the stochastic volatility. It is first shown that it is not possible to formulate this as the usual filtering problem, and an alternative formulation is proposed. A robust filtering equation is then derived suitable for real observation data. Journal: Applied Mathematical Finance Pages: 153-181 Issue: 3 Volume: 7 Year: 2000 Keywords: Stochastic Volatility Hull-WHITE Model Robust Filter, X-DOI: 10.1080/13504860110046074 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110046074 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:3:p:153-181 Template-Type: ReDIF-Article 1.0 Author-Name: Erik Schlogl Author-X-Name-First: Erik Author-X-Name-Last: Schlogl Author-Name: Lutz Schlogl Author-X-Name-First: Lutz Author-X-Name-Last: Schlogl Title: A square root interest rate model fitting discrete initial term structure data Abstract: This paper presents one-factor and multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type 'square root' diffusions with piece wise constant parameters. The model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral chi-square distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices. Journal: Applied Mathematical Finance Pages: 183-209 Issue: 3 Volume: 7 Year: 2000 Keywords: Term Structure Of Interest Rates Fixed Income Derivatives Square Root Process Chi-SQUARE Distribution, X-DOI: 10.1080/13504860110034770 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110034770 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:3:p:183-209 Template-Type: ReDIF-Article 1.0 Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: A PDE approach to risk measures of derivatives Abstract: This paper proposes a partial differential equation (PDE) approach to calculate coherent risk measures for portfolios of derivatives under the Black-Scholes economy. It enables us to define the risk measures in a dynamic way and to deal with American options in a relatively effective way. Our risk measure is based on the representation form of coherent risk measures. Through the use of some earlier results the PDE satisfied by the risk measures are derived. The PDE resembles the standard Black-Scholes type PDE which can be solved using standard techniques from the mathematical finance literature. Indeed, these results reveal that the PDE approach can provide practitioners with a more applicable and flexible way to implement coherent risk measures for derivatives in the context of the Black-Scholes model. Journal: Applied Mathematical Finance Pages: 211-228 Issue: 3 Volume: 7 Year: 2000 Keywords: Coherent Risk Measures American Options Physical Probability Measure Subjective Probability Measures Transaction Costs, X-DOI: 10.1080/13504860110045741 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110045741 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:3:p:211-228 Template-Type: ReDIF-Article 1.0 Author-Name: Henryk Gzyl Author-X-Name-First: Henryk Author-X-Name-Last: Gzyl Title: Maxentropic construction of risk neutral measures: discrete market models Abstract: The maximum entropy principle provides a variational method to select a measure yielding pre-assigned mean values to a random variable. It can also be invoked to construct measures that render a stochastic process a martingale, thus providing a systematic way of constructing risk-neutral measures and thus closing a market. We carry out this programme for discrete market models. On the one hand these are amenable to numerical implementation and on the other, they provide a stepping stone for more general market models in continuous time. Journal: Applied Mathematical Finance Pages: 229-239 Issue: 4 Volume: 7 Year: 2000 X-DOI: 10.1080/13504860110061699 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110061699 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:4:p:229-239 Template-Type: ReDIF-Article 1.0 Author-Name: Roland Mallier Author-X-Name-First: Roland Author-X-Name-Last: Mallier Author-Name: Ghada Alobaidi Author-X-Name-First: Ghada Author-X-Name-Last: Alobaidi Title: Laplace transforms and American options Abstract: Laplace transform methods are used to study the valuation of American call and put options with constant dividend yield, and to derive integral equations giving the location of the optimal exercise boundary. In each case studied, the main result of this paper is a nonlinear Fredholm-type integral equation for the location of the free boundary. The equations differ depending on whether the dividend yield is less than or exceeds the risk-free rate. These integral equations contain a transform variable, so the solution of the equations would involve finding the free boundary that satisfies the equations for all values of this transform variable. Expressions are also given for the transform of the value of the option in terms of this free boundary. Journal: Applied Mathematical Finance Pages: 241-256 Issue: 4 Volume: 7 Year: 2000 Keywords: Laplace Transforms, American Options, Optimal Exercise Boundary, Dividend Yield, Fredholm-TYPE Integral Equation, X-DOI: 10.1080/13504860110060384 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110060384 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:4:p:241-256 Template-Type: ReDIF-Article 1.0 Author-Name: Richard Deaves Author-X-Name-First: Richard Author-X-Name-Last: Deaves Author-Name: Mahmut Parlar Author-X-Name-First: Mahmut Author-X-Name-Last: Parlar Title: A generalized bootstrap method to determine the yield curve Abstract: A new technique is described for operationalizing the bootstrap methodology to estimate the yield curve given any available data set of bond yields. The problem of missing data points is dealt with using symbolic cubic spline interpolation. To make such an approach tractable the computer algebra system Maple is employed to symbolically generate the interpolation equations for the missing data points and to solve the nonlinear equation system in order to obtain the points on the yield curve. Several examples with real data demonstrate the usefulness of the methodology. Journal: Applied Mathematical Finance Pages: 257-270 Issue: 4 Volume: 7 Year: 2000 Keywords: Bootstrap Methodology, Yield Curve, Symbolic Cubic Spline Interpolation, X-DOI: 10.1080/13504860010021162 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860010021162 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:4:p:257-270 Template-Type: ReDIF-Article 1.0 Author-Name: Ryle Perera Author-X-Name-First: Ryle Author-X-Name-Last: Perera Title: The role of index bonds in universal currency hedging Abstract: This study examines the demand for index bonds and their role in hedging risky asset returns against currency risks in a complete market where equity is not hedged against inflation risk. Avellaneda's uncertain volatility model with non-constant coefficients to describe equity price variation, forward price variation, index bond price variation and rate of inflation, together with Merton's intertemporal portfolio choice model, are utilized to enable an investor to choose an optimal portfolio consisting of equity, nominal bonds and index bonds when the rate of inflation is uncertain. A hedge ratio is universal if investors in different countries hedge against currency risk to the same extent. Three universal hedge ratios (UHRs) are defined with respect to the investor's total demand for index bonds, hedging risky asset returns (i.e. equity and nominal bonds) against currency risk, which are not held for hedging purposes. These UHRs are hedge positions in foreign index bond portfolios, stated as a fraction of the national market portfolio. At equilibrium all the three UHRs are comparable to Black's corrected equilibrium hedging ratio. The Cameron-Martin-Girsanov theorem is applied to show that the Radon-Nikodym derivative given under a P -martingale, the investor's exchange rate (product of the two currencies) is a martingale. Therefore the investors can agree on a common hedging strategy to trade exchange rate risk irrespective of investor nationality. This makes the choice of the measurement currency irrelevant and the hedge ratio universal without affecting their values. Journal: Applied Mathematical Finance Pages: 271-284 Issue: 4 Volume: 7 Year: 2000 Keywords: Index Bonds, Universal Currency Hedge Ratio, Uncertain Volatility Model, Intertemporal Portfolio Choice Model, P-MARTINGALE, X-DOI: 10.1080/13504860110058035 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110058035 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:7:y:2000:i:4:p:271-284 Template-Type: ReDIF-Article 1.0 Author-Name: Colin Atkinson Author-X-Name-First: Colin Author-X-Name-Last: Atkinson Author-Name: Sutee Mokkhavesa Author-X-Name-First: Sutee Author-X-Name-Last: Mokkhavesa Title: Towards the determination of utility preference from optimal portfolio selections Abstract: The problem of determining specific utility preference from observed optimal resource allocation procedures is considered. In special cases this is solved completely. Partial solutions and their limitations in this process are also discussed. Journal: Applied Mathematical Finance Pages: 1-26 Issue: 1 Volume: 8 Year: 2001 Keywords: Utility Preference, Optimal Resource Allocation, Partial, Complete Solutions, X-DOI: 10.1080/13504860110039801 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110039801 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:1:p:1-26 Template-Type: ReDIF-Article 1.0 Author-Name: Phelim Boyle Author-X-Name-First: Phelim Author-X-Name-Last: Boyle Author-Name: Ken Seng Tan Author-X-Name-First: Ken Seng Author-X-Name-Last: Tan Author-Name: Weidong Tian Author-X-Name-First: Weidong Author-X-Name-Last: Tian Title: Calibrating the Black-Derman-Toy model: some theoretical results Abstract: The Black-Derman-Toy (BDT) model is a popular one-factor interest rate model that is widely used by practitioners. One of its advantages is that the model can be calibrated to both the current market term structure of interest rate and the current term structure of volatilities. The input term structure of volatility can be either the short term volatility or the yield volatility. Sandmann and Sondermann derived conditions for the calibration to be feasible when the conditional short rate volatility is used. In this paper conditions are investigated under which calibration to the yield volatility is feasible. Mathematical conditions for this to happen are derived. The restrictions in this case are more complicated than when the short rate volatilities are used since the calibration at each time step now involves the solution of two non-linear equations. The theoretical results are illustrated by showing numerically that in certain situations the calibration based on the yield volatility breaks down for apparently plausible inputs. In implementing the calibration from period n to period n + 1, the corresponding yield volatility has to lie within certain bounds. Under certain circumstances these bounds become very tight. For yield volatilities that violate these bounds, the computed short rates for the period (n, n + 1) either become negative or else explode and this feature corresponds to the economic intuition behind the breakdown. Journal: Applied Mathematical Finance Pages: 27-48 Issue: 1 Volume: 8 Year: 2001 Keywords: Interest Rate Models, Black-DERMAN-TOY Model, Volatility, Short Term, Yield, X-DOI: 10.1080/13504860110062049 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110062049 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:1:p:27-48 Template-Type: ReDIF-Article 1.0 Author-Name: Y. D'Halluin Author-X-Name-First: Y. Author-X-Name-Last: D'Halluin Author-Name: P. A. Forsyth Author-X-Name-First: P. A. Author-X-Name-Last: Forsyth Author-Name: K. R. Vetzal Author-X-Name-First: K. R. Author-X-Name-Last: Vetzal Author-Name: G. Labahn Author-X-Name-First: G. Author-X-Name-Last: Labahn Title: A numerical PDE approach for pricing callable bonds Abstract: Many debt issues contain an embedded call option that allows the issuer to redeem the bond at specified dates for a specified price. The issuer is typically required to provide advance notice of a decision to exercise this call option. The valuation of these contracts is an interesting numerical exercise because discontinuities may arise in the bond value or its derivative at call and/or notice dates. Recently, it has been suggested that finite difference methods cannot be used to price callable bonds requiring notice. Poor accuracy was attributed to discontinuities and difficulties in handling boundary conditions. As an alternative, a semi-analytical method using Green's functions for valuing callable bonds with notice was proposed. Unfortunately, the Green's function method is limited to special cases. Consequently, it is desirable to develop a more general approach. This is provided by using more advanced techniques such as flux limiters to obtain an accurate numerical partial differential equation method. Finally, in a typical pricing model an inappropriate financial condition is required in order to properly specify boundary conditions for the associated PDE. It is shown that a small perturbation of such a model is free from such artificial conditions. Journal: Applied Mathematical Finance Pages: 49-77 Issue: 1 Volume: 8 Year: 2001 Keywords: Callable Bond, Numerical Pde, Discontinuity, Green'S Function, X-DOI: 10.1080/13504860110046885 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110046885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:1:p:49-77 Template-Type: ReDIF-Article 1.0 Author-Name: Umberto Cherubini Author-X-Name-First: Umberto Author-X-Name-Last: Cherubini Author-Name: Giovanni Della Lunga Author-X-Name-First: Giovanni Author-X-Name-Last: Della Lunga Title: Liquidity and credit risk Abstract: The paper uses fuzzy measure theory to represent liquidity risk, i.e. the case in which the probability measure used to price contingent claims is not known precisely. This theory enables one to account for different values of long and short positions. Liquidity risk is introduced by representing the upper and lower bound of the price of the contingent claim computed as the upper and lower Choquet integral with respect to a subadditive function. The use of a specific class of fuzzy measures, known as g λ measures enables one to easily extend the available asset pricing models to the case of illiquid markets. As the technique is particularly useful in corporate claims evaluation, a fuzzified version of Merton's model of credit risk is presented. Sensitivity analysis shows that both the level and the range (the difference between upper and lower bounds) of credit spreads are positively related to the 'quasi debt to firm value ratio' and to the volatility of the firm value. This finding may be read as correlation between credit risk and liquidity risk, a result which is particularly useful in concrete risk-management applications. The model is calibrated on investment grade credit spreads, and it is shown that this approach is able to reconcile the observed credit spreads with risk premia consistent with observed default rate. Default probability ranges, rather than point estimates, seem to play a major role in the determination of credit spreads. Journal: Applied Mathematical Finance Pages: 79-95 Issue: 2 Volume: 8 Year: 2001 Keywords: Credit Risk, Incomplete Markets, Liquidity Risk, Knightian Uncertainty, Option Pricing, Fuzzy Measures, X-DOI: 10.1080/13504860110061013 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110061013 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:2:p:79-95 Template-Type: ReDIF-Article 1.0 Author-Name: Vicky Henderson Author-X-Name-First: Vicky Author-X-Name-Last: Henderson Author-Name: David Hobson Author-X-Name-First: David Author-X-Name-Last: Hobson Title: Passport options with stochastic volatility Abstract: A passport option is a call option on the profits of a trading account. In this article, the robustness of passport option pricing is investigated by incorporating stochastic volatility. The key feature of a passport option is the holders' optimal strategy. It is known that in the case of exponential Brownian motion the strategy is to be long if the trading account is below zero and short if the account is above zero. Here this result is extended to models with stochastic volatility where the volatility is defined via an autonomous SDE. It is shown that if the Brownian motions driving the underlying asset and the volatility are independent then the form of the optimal strategy remains unchanged. This means that the strategy is robust to misspecification of the underlying model. A second aim of this article is to investigate some of the biases which become apparent in a stochastic volatility regime. Using an analytic approximation, comparisons are obtained for passport option prices using the exponential Brownian motion model and some well-known stochastic volatility models. This is illustrated with numerical examples. One conclusion is that if volatility and price are uncorrelated, then prices are sometimes lower in a model with stochastic volatility than in a model with constant volatility. Journal: Applied Mathematical Finance Pages: 97-118 Issue: 2 Volume: 8 Year: 2001 Keywords: Passport Option, Option Pricing, Stochastic Volatility, Hull And White Model, X-DOI: 10.1080/13504860110068863 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110068863 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:2:p:97-118 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Howison Author-X-Name-First: Sam Author-X-Name-Last: Howison Author-Name: David Lamper Author-X-Name-First: David Author-X-Name-Last: Lamper Title: Trading volume in models of financial derivatives Abstract: This paper develops a subordinated stochastic process model for an asset price, where the directing process is identified as information. Motivated by recent empirical and theoretical work, the paper makes use of the under-used market statistic of transaction count as a suitable proxy for the information flow. An option pricing formula is derived, and comparisons with stochastic volatility models are drawn. Both the asset price and the number of trades are used in parameter estimation. The underlying process is found to be fast mean reverting, and this is exploited to perform an asymptotic expansion. The implied volatility skew is then used to calibrate the model. Journal: Applied Mathematical Finance Pages: 119-135 Issue: 2 Volume: 8 Year: 2001 Keywords: Trading Volume, Subordinated Process, Stochastic Volatility, Option Pricing, X-DOI: 10.1080/13504860110074163 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110074163 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:2:p:119-135 Template-Type: ReDIF-Article 1.0 Author-Name: Laura Ballotta Author-X-Name-First: Laura Author-X-Name-Last: Ballotta Author-Name: Andreas Kyprianou Author-X-Name-First: Andreas Author-X-Name-Last: Kyprianou Title: A note on the α-quantile option Abstract: Some properties of a class of path-dependent options based on the α-quantiles of Brownian motion are discussed. In particular, it is shown that such options are well behaved in relation to standard options and comparatively cheaper than an equivalent class of lookback options. Journal: Applied Mathematical Finance Pages: 137-144 Issue: 3 Volume: 8 Year: 2001 Keywords: Alpha-QUANTILE Of Brownian Motions With Drift, Dassios-PORT-WENDEL Identity, Fixed Strike Lookback Option, X-DOI: 10.1080/13504860210122375 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210122375 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:3:p:137-144 Template-Type: ReDIF-Article 1.0 Author-Name: David Prieul Author-X-Name-First: David Author-X-Name-Last: Prieul Author-Name: Vladislav Putyatin Author-X-Name-First: Vladislav Author-X-Name-Last: Putyatin Author-Name: Tarek Nassar Author-X-Name-First: Tarek Author-X-Name-Last: Nassar Title: On pricing and reserving with-profits life insurance contracts Abstract: As a first approximation, asset and liability management issues faced by life insurance companies originate from the sale of with-profits contracts. These contracts are bond-type products with several rate guarantees and other interestsensitive embedded options. Benefits paid out to policyholders mostly depend on the investment performance of a given asset portfolio in which premiums are invested. Thus, guarantees and options granted to policyholders may become effective when the investment performance of the asset portfolio is poor. Issuing a with-profits contract is therefore not equivalent to issuing plain-vanilla debt. The purpose of this paper is to value with-profits liabilities in a consistent option-pricing framework and to develop efficient asset or liability strategies to manage profitability and variability of shareholder value. Journal: Applied Mathematical Finance Pages: 145-166 Issue: 3 Volume: 8 Year: 2001 Keywords: Asset And Liability Management, Life Insurance, With-PROFITS Policy, Shareholder Value, Option Pricing, Parabolic Partial Differential Equations, Matched Asymptotic Expansions, X-DOI: 10.1080/13504860110111279 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110111279 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:3:p:145-166 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Siegl Author-X-Name-First: Thomas Author-X-Name-Last: Siegl Author-Name: Ansgar West Author-X-Name-First: Ansgar Author-X-Name-Last: West Title: Statistical bootstrapping methods in VaR calculation Abstract: Monte Carlo methods are often applied to problems in finance especially in the area of risk calculation by the Value-atRisk (VaR) measure. Different applications of statistical resampling techniques are shown, specifically bootstrapping, to refine the computational results in different ways. Methods are provided for improving backtesting stability, acceleration of Monte Carlo VaR convergence by orders of magnitude, and incorporating covariance matrix uncertainty in VaR figures. Existing methods are applied and new solutions developed. Extensive numerical tests on large numbers of randomly generated portfolios prove the effectiveness of the suggested solutions. Journal: Applied Mathematical Finance Pages: 167-181 Issue: 3 Volume: 8 Year: 2001 Keywords: Value-AT-RISK, Monte Carlo, Resampling, Variance Reduction, Finance, X-DOI: 10.1080/13504860110093504 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110093504 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:3:p:167-181 Template-Type: ReDIF-Article 1.0 Author-Name: Victor Vaugirard Author-X-Name-First: Victor Author-X-Name-Last: Vaugirard Title: Monte Carlo applied to exotic digital options Abstract: This paper tailors Monte Carlo simulations to the scope of binary options whose underlying dynamics obey jump-diffusion or jump-mean-reverting processes and may not be traded. In the process, the existence of well-defined arbitrage prices is justified notwithstanding a framework of incomplete markets. The all-or-nothing feature of digital options makes simulations unstable in the vicinity of their threshold, which entails the implementation of variance reduction techniques. An extension to stochastic interest rates highlights the fact that probabilistic techniques and simulations can be married to further improve the accuracy of the estimations. Journal: Applied Mathematical Finance Pages: 183-196 Issue: 3 Volume: 8 Year: 2001 Keywords: Mean-REVERTING Process, Jump-DIFFUSION Process, Control Variate Method, Antithetic Technique, Change Of Numeraire, X-DOI: 10.1080/13504860110115194 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860110115194 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:3:p:183-196 Template-Type: ReDIF-Article 1.0 Author-Name: Grant Armstrong Author-X-Name-First: Grant Author-X-Name-Last: Armstrong Title: Valuation formulae for window barrier options Abstract: In this paper we study window barrier options, where a single constant continuously-monitored barrier prevails for a period that commences strictly after the start date of the option and terminates strictly before expiry. We determine valuation formulae within a limited deterministic term-structure in terms of trivariate normal distribution functions. These formulae offer a generalization of the valuation formulae for partial barrier options given by Heynan and Kat. Journal: Applied Mathematical Finance Pages: 197-208 Issue: 4 Volume: 8 Year: 2001 Keywords: Window Barrier Options, Convolution Density, Option Valuation Formulae, Trivariate Normal Distribution, X-DOI: 10.1080/13504860210124607 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210124607 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:4:p:197-208 Template-Type: ReDIF-Article 1.0 Author-Name: Tristan Guillaume Author-X-Name-First: Tristan Author-X-Name-Last: Guillaume Title: valuation of options on joint minima and maxima Abstract: It is shown how to obtain explicit formulae for a variety of popular path-dependent contracts with complex payoffs involving joint distributions of several extrema. More specifically, formulae are given for standard step-up and stepdown barrier options, as well as partial and outside step-up and step-down barrier options, between three and five dimensions. The proposed method can be extended to other exotic path-dependent payoffs as well as to higher dimensions. Numerical results show that the quasi-random integration of these formulae, involving multivariate distributions of correlated Gaussian random variables, provides option values more quickly and more accurately than Monte Carlo simulation. Journal: Applied Mathematical Finance Pages: 209-233 Issue: 4 Volume: 8 Year: 2001 Keywords: Dimensionality, Joint Extrema, Step Barrier Options, Quasi-RANDOM Integration, X-DOI: 10.1080/13504860210122384 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210122384 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:4:p:209-233 Template-Type: ReDIF-Article 1.0 Author-Name: Christian Zuhlsdorff Author-X-Name-First: Christian Author-X-Name-Last: Zuhlsdorff Title: The pricing of derivatives on assets with quadratic volatility Abstract: The basic model of financial economics is the Samuelson model of geometric Brownian motion because of the celebrated Black-Scholes formula for pricing the call option. The asset's volatility is a linear function of the asset value and the model guarantees positive asset prices. In this paper, it is shown that the pricing partial differential equation can be solved for level-dependent volatility which is a quadratic polynomial. If zero is attainable, both absorption and negative asset values are possible. Explicit formulae are derived for the call option: a generalization of the Black-Scholes formula for an asset whose volatiliy is affine, the formula for the Bachelier model with constant volatility, and new formulae in the case of quadratic volatility. The implied Black-Scholes volatilities of the Bachelier and the affine model are frowns, the quadratic specifications imply smiles. Journal: Applied Mathematical Finance Pages: 235-262 Issue: 4 Volume: 8 Year: 2001 Keywords: Strong Solutions, Stochastic Differential Equation, Option Pricing, Quadratic Volatility, Implied Volatility, Smiles, Frowns, X-DOI: 10.1080/13504860210127271 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210127271 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:8:y:2001:i:4:p:235-262 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Alaton Author-X-Name-First: Peter Author-X-Name-Last: Alaton Author-Name: Boualem Djehiche Author-X-Name-First: Boualem Author-X-Name-Last: Djehiche Author-Name: David Stillberger Author-X-Name-First: David Author-X-Name-Last: Stillberger Title: On modelling and pricing weather derivatives Abstract: The main objective of the work described is to find a pricing model for weather derivatives with payouts depending on temperature. Historical data are used to suggest a stochastic process that describes the evolution of the temperature. Since temperature is a non-tradable quantity, unique prices of contracts in an incomplete market are obtained using the market price of risk. Numerical examples of prices of some contracts are presented, using an approximation formula as well as Monte Carlo simulations. Journal: Applied Mathematical Finance Pages: 1-20 Issue: 1 Volume: 9 Year: 2002 Keywords: Weather Derivatives, Pricing Model, Historical Data, Stochastic Process, Approximation Formula, Monte Carlo Simulation, X-DOI: 10.1080/13504860210132897 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210132897 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Mihaela Manoliu Author-X-Name-First: Mihaela Author-X-Name-Last: Manoliu Author-Name: Stathis Tompaidis Author-X-Name-First: Stathis Author-X-Name-Last: Tompaidis Title: Energy futures prices: term structure models with Kalman filter estimation Abstract: We present a class of multi-factor stochastic models for energy futures prices, similar to the interest rate futures models recently formulated by Heath. We do not postulate directly the risk-neutral processes followed by futures prices, but define energy futures prices in terms of a spot price, not directly observable, driven by several stochastic factors. Our formulation leads to an expression for futures prices which is well suited to the application of Kalman filtering techniques together with maximum likelihood estimation methods. Based on these techniques, we perform an empirical study of a one- and a two-factor model for futures prices for natural gas. Journal: Applied Mathematical Finance Pages: 21-43 Issue: 1 Volume: 9 Year: 2002 Keywords: Multi-FACTOR Term Structure Models, Kalman Filter Estimation, X-DOI: 10.1080/13504860210126227 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210126227 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:1:p:21-43 Template-Type: ReDIF-Article 1.0 Author-Name: Iivo Vehvilainen Author-X-Name-First: Iivo Author-X-Name-Last: Vehvilainen Title: Basics of electricity derivative pricing in competitive markets Abstract: This paper studies the application of the available financial theory to the deregulated electricity market. The special characteristics of electricity make the market different from all other commodity markets. The paper introduces a coherent framework for the assets and instruments in the electricity markets in the financial tradition. Properties of the instruments that are available in the Scandinavian electricity market are studied in more detail. Journal: Applied Mathematical Finance Pages: 45-60 Issue: 1 Volume: 9 Year: 2002 Keywords: Electricity Derivatives, Electricity Forwards, Exotic Options, Pricing, X-DOI: 10.1080/13504860210132879 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210132879 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:1:p:45-60 Template-Type: ReDIF-Article 1.0 Author-Name: A. Leon Author-X-Name-First: A. Author-X-Name-Last: Leon Author-Name: J. E. Peris Author-X-Name-First: J. E. Author-X-Name-Last: Peris Author-Name: J. Silva Author-X-Name-First: J. Author-X-Name-Last: Silva Author-Name: B. Subiza Author-X-Name-First: B. Author-X-Name-Last: Subiza Title: A note on adjusting correlation matrices Abstract: A new algorithm for adjusting correlation matrices and for comparison with Finger's algorithm, which is used to compute Value-at-Risk in RiskMetrics for stress test scenarios. The solution proposed by the new methodology is always better than Finger's approach in the sense that it alters as little as possible those correlations that one would wish not to alter, but they change in order to obtain a consistent Finger correlation matrix. Journal: Applied Mathematical Finance Pages: 61-67 Issue: 1 Volume: 9 Year: 2002 Keywords: Correlation Matrix, Kuhn-TUCKER Conditions, Eigenvalue, Value-AT-RISK, X-DOI: 10.1080/13504860210136721 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210136721 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:1:p:61-67 Template-Type: ReDIF-Article 1.0 Author-Name: U. Cherubini Author-X-Name-First: U. Author-X-Name-Last: Cherubini Author-Name: E. Luciano Author-X-Name-First: E. Author-X-Name-Last: Luciano Title: Bivariate option pricing with copulas Abstract: The adoption of copula functions is suggested in order to price bivariate contingent claims. Copulas enable the marginal distributions extracted from vertical spreads in the options markets to be imbedded in a multivariate pricing kernel. It is proved that such a kernel is a copula function, and that its super-replication strategy is represented by the Frechet bounds. Applications provided include prices for binary digital options, options on the minimum and options to exchange one asset for another. For each of these products, no-arbitrage pricing bounds, as well as values consistent with the independence of the underlying assets are provided. As a final reference value, a copula function calibrated on historical data is used. Journal: Applied Mathematical Finance Pages: 69-85 Issue: 2 Volume: 9 Year: 2002 Keywords: Bivariate Option Pricing, Copula Functions, Pricing Kernel, Applications, X-DOI: 10.1080/13504860210136721a File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210136721a File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:2:p:69-85 Template-Type: ReDIF-Article 1.0 Author-Name: C. Mancini Author-X-Name-First: C. Author-X-Name-Last: Mancini Title: The European options hedge perfectly in a Poisson-Gaussian stock market model Abstract: It is shown that n + 1 European call options written on a stock S with different strike prices (or the stock and n calls) are non-redundant assets in a model for the stock driven by a Brownian motion and n independent Poisson processes. That extends the result obtained for n = 1 by Pham and implies that the proposed model can price and perfectly hedge any integrable derivative on S. Journal: Applied Mathematical Finance Pages: 87-102 Issue: 2 Volume: 9 Year: 2002 Keywords: Jump-DIFFUSION Stock Model, M-VARIATE Poisson Process, Call Options, Volatility Coefficients, T-BASIS, Total Convergence, Completeness, X-DOI: 10.1080/13504860210148241 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210148241 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:2:p:87-102 Template-Type: ReDIF-Article 1.0 Author-Name: Jun Sekine Author-X-Name-First: Jun Author-X-Name-Last: Sekine Title: On superhedging under delta constraints Abstract: The superhedging problem of derivative securities under the constraint of portfolio amounts is revisited. This paper considers more general forms of constraints, characterizes the minimal superhedging cost using a 'dual' maximization problem, and shows that a replicating strategy of the so-called 'face-lifted' claim gives a minimal superhedging strategy in the European option case. Also, as hinted by the static-replication technique, a superhedging strategy is computed for a knockout option in closed form. Journal: Applied Mathematical Finance Pages: 103-121 Issue: 2 Volume: 9 Year: 2002 Keywords: Superhedging, Delta Constraint, Duality Method, Knockout Option, X-DOI: 10.1080/13504860210150941 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210150941 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:2:p:103-121 Template-Type: ReDIF-Article 1.0 Author-Name: Adam Smith Author-X-Name-First: Adam Author-X-Name-Last: Smith Title: American options under uncertain volatility Abstract: The uncertain volatility approach to financial derivatives is extended to American options (which allow early exercise before expiry). The requirement to model at the portfolio level made necessary by the non-linearity of the approach is found to lead to a recursive structure to the exercise possibilities across options. Other novel features include: the optimality sometimes of partial exercise; an interesting resolution to the issues surrounding short options whose exercise is controlled by a buyer counterparty; and the occurrence of a simple game structure for portfolios containing both long and short options. It is demonstrated that the exercise strategies resulting can significantly alter measured uncertain volatility risk. Contrary to the set of attributes for sensible risk measures put forward by Artzner, Delbaen, Eber and Heath, this risk need not be homogenous in portfolio size- forming a convincing argument for weakening this particular requirement. Journal: Applied Mathematical Finance Pages: 123-141 Issue: 2 Volume: 9 Year: 2002 Keywords: Optimal Exercise, Partial Exercise, Derivatives Risk Measurement, X-DOI: 10.1080/13504860210136730 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210136730 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:2:p:123-141 Template-Type: ReDIF-Article 1.0 Author-Name: Fernando Fernandez-Rodriguez Author-X-Name-First: Fernando Author-X-Name-Last: Fernandez-Rodriguez Author-Name: Maria-Dolores Garcia-Artiles Author-X-Name-First: Maria-Dolores Author-X-Name-Last: Garcia-Artiles Author-Name: Juan Manuel Martin-Gonzalez Author-X-Name-First: Juan Manuel Author-X-Name-Last: Martin-Gonzalez Title: A model of speculative behaviour with a strange attractor Abstract: An asset pricing model for a speculative financial market with fundamentalists and chartists is analysed. The model explains bursts of volatility in financial markets, which are not well explained by the traditional finance paradigms. Speculative bubbles arise as a complex non-linear dynamic phenomenon brought about naturally by the dynamic interaction of heterogeneous market participants. Depending on the time lag in the formation of chartists' expectations, the system evolves through several dynamic regimes, finishing in a strange attractor. Chaos provides a self-sustained motion around the rationally expected equilibrium that corresponds to a speculative bubble. In order to explain the role of Chartism, chaotic motion is a very interesting theoretical feature for a speculative financial market model. It provides a complex non-linear dynamic behaviour around the Walrasian equilibrium price produced by deterministic interactions between fundamentalists and chartists. This model could be a link between two opposite views over the behaviour of financial markets: the theorist's literature view that claims the random motion of asset prices, and the chartist's position extensively adopted by market professionals. Journal: Applied Mathematical Finance Pages: 143-161 Issue: 3 Volume: 9 Year: 2002 Keywords: Bubbles, Technical Analysis, Charting, Market Speculation, Deterministic Chaos, X-DOI: 10.1080/13504860210159032 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210159032 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:3:p:143-161 Template-Type: ReDIF-Article 1.0 Author-Name: David Heath Author-X-Name-First: David Author-X-Name-Last: Heath Author-Name: Stefano Herzel Author-X-Name-First: Stefano Author-X-Name-Last: Herzel Title: Efficient option valuation using trees Abstract: An algorithm is proposed for the discrete approximation of continuous market price processes that uses trees instead of lattices. It is shown that it is convergent when used for pricing both European and American options and that it is more efficient, for some models, than the usual recombining schemes. Journal: Applied Mathematical Finance Pages: 163-178 Issue: 3 Volume: 9 Year: 2002 Keywords: Option Pricing, Discrete-TIME Approximations, Non-RECOMBINING Trees, X-DOI: 10.1080/13504860210146711 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210146711 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:3:p:163-178 Template-Type: ReDIF-Article 1.0 Author-Name: Roy Kluitman Author-X-Name-First: Roy Author-X-Name-Last: Kluitman Author-Name: Philip Hans Franses Author-X-Name-First: Philip Hans Author-X-Name-Last: Franses Title: Estimating volatility on overlapping returns when returns are autocorrelated Abstract: Overlapping financial returns are sometimes used to increase the efficiency and power of statistical tests and for Value-at-Risk analysis. This is particularly useful when there are not many observations, such as daily returns for emerging markets. Sometimes, returns show autocorrelation. In this paper, unbiased variance estimators are derived for overlapping returns when the returns are generated by AR(1) or MA(1) processes. A limited Monte Carlo experiment reveals that alternative estimators can suffer from substantial bias. The relevance of using proper estimators is emphasized by considering daily returns for six emerging markets. Journal: Applied Mathematical Finance Pages: 179-188 Issue: 3 Volume: 9 Year: 2002 Keywords: Asset Returns, Random Walk, First-ORDER Dynamics, Overlapping Returns, X-DOI: 10.1080/13504860210162029 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860210162029 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:3:p:179-188 Template-Type: ReDIF-Article 1.0 Author-Name: Faouzi Trabelsi Author-X-Name-First: Faouzi Author-X-Name-Last: Trabelsi Author-Name: Abdelhamid Trad Author-X-Name-First: Abdelhamid Author-X-Name-Last: Trad Title: L 2 -discrete hedging in a continuous-time model Abstract: In the setting of the Black-Scholes option pricing market model, the seller of a European option must trade continuously in time. This is, of course, unrealistic from the practical viewpoint. He must then follow a discrete trading strategy. However, it does not seem natural to hedge at deterministic times regardless of moves of the spot price. In this paper, it is supposed that the hedger trades at a fixed number N of rebalancing (stopping) times. The problem (PN) of selecting the optimal hedging times and ratios which allow one to minimize the variance of replication error is considered. For given N rebalancing, the discrete optimal hedging strategy is identified for this criterion. The problem (PN) is then transformed into a multidimensional optimal stopping problem with boundary constraints. The restrictive problem (PNBS) of selecting the optimal rebalancing for the same criterion is also considered when the ratios are given by Black-Scholes. Using the vector-valued optimal stopping theory, the existence is shown of an optimal sequence of rebalancing for each one of the problems (PN) and (PNBS). It also shown BS that they are asymptotically equivalent when the number of rebalances becomes large and an optimality criterion is stated for the problem (PN). The same study is made when more realistic restrictions are imposed on the hedging times. In the special case of two rebalances, the problem (P2BS) is solved and the problems (P2BS) and (P2) are transformed into two optimal stopping problems. This transformation is useful for numerical purposes. Journal: Applied Mathematical Finance Pages: 189-217 Issue: 3 Volume: 9 Year: 2002 Keywords: Discrete Hedging, Black-SCHOLES Model, Variance Of Replication Error, Multidimensional Optimal Stopping Problems, Optimality Criterion, X-DOI: 10.1080/1350486022000013672 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486022000013672 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:3:p:189-217 Template-Type: ReDIF-Article 1.0 Author-Name: Shaun Bond Author-X-Name-First: Shaun Author-X-Name-Last: Bond Author-Name: Stephen Satchell Author-X-Name-First: Stephen Author-X-Name-Last: Satchell Title: Statistical properties of the sample semi-variance Abstract: In finance theory the standard deviation of asset returns is almost universally recognized as a measure of risk. This universality continues to exist even in the presence of known limitations of using the standard deviation and also an extensive and growing literature on alternative risk measures. One possible reason for this persistence is that the sample properties of alternative risk measures are not well understood. This paper attempts to compare the sample distribution of the semi-variance with that of the variance. In particular, the belief that, while there are convincing theoretical reasons to use the semi-variance the volatility of the sample measure is so high as to make the measure impractical in applied work, is investigated. In addition arguments based on stochastic dominance are also used to compare the distribution of the two statistics. Conditions are developed to identify situations in which the semi-variance may be preferred to the variance. An empirical example using equity data from emerging markets demonstrates this approach. Journal: Applied Mathematical Finance Pages: 219-239 Issue: 4 Volume: 9 Year: 2002 Keywords: Downside Risk, Semi-VARIANCE, Stochastic Dominance, Risk Measures, Emerging, Markets, X-DOI: 10.1080/1350486022000015850 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486022000015850 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:219-239 Template-Type: ReDIF-Article 1.0 Author-Name: Andrea Gam Author-X-Name-First: Andrea Author-X-Name-Last: Gam Author-Name: Paolo Pellizzari Author-X-Name-First: Paolo Author-X-Name-Last: Pellizzari Title: Utility based pricing of contingent claims in incomplete markets Abstract: In a discrete setting, a model is developed for pricing a contingent claim in incomplete markets. Since hedging opportunities influence the price of a contingent claim, the optimal hedging strategy is first introduced assuming that a contingent claim has been issued: a strategy implemented by investing initial wealth plus the selling price is optimal if it maximizes the expected utility of the agent's net payoff, which is the difference between the outcome of the hedging portfolio and the payoff of the claim. The 'reservation price' is then introduced as a subjective valuation of a contingent claim. This is defined as the minimum price that makes the issue of the claim preferable to staying put given that, once the claim has been written, the writer hedges it according to the expected utility criterion. The reservation price is defined both for a short position (reservation selling price) and for a long position (reservation buying price) in the claim. When the contingent claim is redundant, both the selling and the buying price collapse in the usual Arrow-Debreu (or Black-Scholes) price. If the claim is non-redundant, then the reservation prices are interior points of the bid-ask interval. Two numerical examples are provided with different utility functions and contingent claims. Some qualitative properties of the reservation price are shown. Journal: Applied Mathematical Finance Pages: 241-260 Issue: 4 Volume: 9 Year: 2002 Keywords: Contingent Claims, Incomplete Markets, Reservation Price, Expected Utility, Optimization, X-DOI: 10.1080/1350486021000029255 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486021000029255 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:241-260 Template-Type: ReDIF-Article 1.0 Author-Name: Mattias Jonsson Author-X-Name-First: Mattias Author-X-Name-Last: Jonsson Author-Name: Jussi Keppo Author-X-Name-First: Jussi Author-X-Name-Last: Keppo Title: Option pricing for large agents Abstract: This paper considers arbitrage-free option pricing in the presence of large agents. These large agents have a significant market power, and their trading strategies influence the dynamics of the financial asset prices. First, a simple asset pricing model in the presence of large agents is presented. Then a nonlinear partial differential equation is found for the prices of European options in the model. The unit option price depends on the large agent's asset holdings. Finally, a game model is introduced for the interaction between different market players. In this game, the outstanding number of options, as well as the option price, is found as a Nash equilibrium. Journal: Applied Mathematical Finance Pages: 261-272 Issue: 4 Volume: 9 Year: 2002 X-DOI: 10.1080/1350486022000025471 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486022000025471 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:261-272 Template-Type: ReDIF-Article 1.0 Author-Name: James Sfiridis Author-X-Name-First: James Author-X-Name-Last: Sfiridis Author-Name: Alan Gelfand Author-X-Name-First: Alan Author-X-Name-Last: Gelfand Title: A survey of sampling-based Bayesian analysis of financial data Abstract: The capability of implementing a complete Bayesian analysis of experimental data has emerged over recent years due to computational advances developed within the statistical community. The objective of this paper is to provide a practical exposition of these methods in the illustrative context of a financial event study. The customary assumption of Gaussian errors underlying development of the model is later supplemented by considering Student-t errors, thus permitting a Bayesian sensitivity analysis. The supplied data analysis illustrates the advantages of the sampling-based Bayesian approach in allowing investigation of quantities beyond the scope of classical methods. Journal: Applied Mathematical Finance Pages: 273-291 Issue: 4 Volume: 9 Year: 2002 Keywords: Event Studies, Inference, Bayesian, Markov Chain Monte Carlo, Gibbs Sampler, X-DOI: 10.1080/1350486022000026885 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486022000026885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:9:y:2002:i:4:p:273-291 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Almgren Author-X-Name-First: Robert Author-X-Name-Last: Almgren Title: Optimal execution with nonlinear impact functions and trading-enhanced risk Abstract: Optimal trading strategies are determined for liquidation of a large single-asset portfolio to minimize a combination of volatility risk and market impact costs. The market impact cost per share is taken to be a power law function of the trading rate, with an arbitrary positive exponent. This includes, for example, the square root law that has been proposed based on market microstructure theory. In analogy to the linear model, a 'characteristic time' for optimal trading is defined, which now depends on the initial portfolio size and decreases as execution proceeds. A model is also considered in which uncertainty of the realized price is increased by demanding rapid execution; it is shown that optimal trajectories are described by a 'critical portfolio size' above which this effect is dominant and below which it may be neglected. Journal: Applied Mathematical Finance Pages: 1-18 Issue: 1 Volume: 10 Year: 2003 Keywords: Market Impact, Trading Strategy, Liquidity Modeling, X-DOI: 10.1080/135048602100056 File-URL: http://www.tandfonline.com/doi/abs/10.1080/135048602100056 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:1-18 Template-Type: ReDIF-Article 1.0 Author-Name: Mahmoud Hamada Author-X-Name-First: Mahmoud Author-X-Name-Last: Hamada Author-Name: Michael Sherris Author-X-Name-First: Michael Author-X-Name-Last: Sherris Title: Contingent claim pricing using probability distortion operators: methods from insurance risk pricing and their relationship to financial theory Abstract: This paper considers the pricing of contingent claims using an approach developed and used in insurance pricing. The approach is of interest and significance because of the increased integration of insurance and financial markets and also because insurance-related risks are trading in financial markets as a result of securitization and new contracts on futures exchanges. This approach uses probability distortion functions as the dual of the utility functions used in financial theory. The pricing formula is the same as the Black-Scholes formula for contingent claims when the underlying asset price is log-normal. The paper compares the probability distortion function approach with that based on financial theory. The theory underlying the approaches is set out and limitations on the use of the insurance-based approach are illustrated. The probability distortion approach is extended to the pricing of contingent claims for more general assumptions than those used for Black-Scholes option pricing. Journal: Applied Mathematical Finance Pages: 19-47 Issue: 1 Volume: 10 Year: 2003 Keywords: Contingent Claim Pricing, Probability Distortion Functions, Non-expected Utility, Insurance Pricing, Black And Sholes, X-DOI: 10.1080/1350486032000069580 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000069580 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:19-47 Template-Type: ReDIF-Article 1.0 Author-Name: Atsushi Kawai Author-X-Name-First: Atsushi Author-X-Name-Last: Kawai Title: A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach Abstract: This paper presents a new approximate pricing formula for European payer swaptions in the LIBOR market model using an asymptotic expansion method. The formula is very flexible, since it can be applied to a wide range of volatility functions. The formula is tested with a log-normal volatility function and a modified CEV volatility function. Numerical results show that the proposed approximate formula is more accurate than other approximate formulae. Journal: Applied Mathematical Finance Pages: 49-74 Issue: 1 Volume: 10 Year: 2003 Keywords: Libor Market Model, Swaptions, Asymptotic Expansion, Monte Carlo Simulation, Volatility Skews, X-DOI: 10.1080/1350486021000029216 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486021000029216 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:49-74 Template-Type: ReDIF-Article 1.0 Author-Name: Victor Vaugirard Author-X-Name-First: Victor Author-X-Name-Last: Vaugirard Title: Valuing catastrophe bonds by Monte Carlo simulations Abstract: This paper reports fairly accurate simulations of insurance-linked securities within an arbitrage-free framework, while accounting for catastrophic events and allowing for stochastic interest rates. Assessing these contingent claims exhibits features of instability rooted in the discontinuity of the payoffs of binary options around their threshold, which is magnified by possible jumps in their underlying dynamics. The error made while simulating path-dependent digital options whose underlyings obey geometric Brownian motion is used to control the estimation of digital options whose underlyings follow jump-diffusion processes. Comparative statics results highlight the hump shape of the term structure of catbond yield spreads. Journal: Applied Mathematical Finance Pages: 75-90 Issue: 1 Volume: 10 Year: 2003 Keywords: Catastrophe Bonds, Digital Options, Jump-diffusion Process, Mean-reverting Process, Variance Reduction, X-DOI: 10.1080/1350486032000079741 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000079741 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:1:p:75-90 Template-Type: ReDIF-Article 1.0 Author-Name: Nathan Berg Author-X-Name-First: Nathan Author-X-Name-Last: Berg Author-Name: Donald Lien Author-X-Name-First: Donald Author-X-Name-Last: Lien Title: Tracking error decision rules and accumulated wealth Abstract: There is compelling evidence that typical decision-makers, including individual investors and even professional money managers, care about the difference between their portfolio returns and a reference point, or benchmark return. In the context of financial markets, likely benchmarks against which investors compare their own returns include easy-to-focus-on numbers such as one's own past payoffs, historical average payoffs, and the payoffs of competitors. Referring to the gap between one's current portfolio return and the benchmark return as 'tracking error', this paper develops a simple model to study the consequences and possible origins of investors who use expected tracking error to guide their portfolio decisions, referred to as 'tracking error types'. In particular, this paper analyses the level of risk-taking and accumulated wealth of tracking error types using standard mean-variance investors as a comparison group. The behaviour of these two types are studied first in isolation, and then in an equilibrium model. Simple analytic results together with statistics summarizing simulated wealth accumulations point to the conclusion that tracking error—whether it is interpreted as reflecting inertia, habituation, or a propensity to make social comparisons in evaluating one's own performance—leads to greater risk-taking and greater shares of accumulated wealth. This result holds even though the two types are calibrated to be identically risk-averse when expected tracking error equals zero. In the equilibrium model, increased aggregate levels of risk-taking reduce the returns on risk. Therefore, the net social effect of tracking-error-induced risk-taking is potentially ambiguous. This paper shows, however, that tracking error promotes a pattern of specialization that helps the economy move towards the path of maximum accumulated wealth. Journal: Applied Mathematical Finance Pages: 91-119 Issue: 2 Volume: 10 Year: 2003 X-DOI: 10.1080/1350486032000088912 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000088912 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:2:p:91-119 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Ericsson Author-X-Name-First: Jan Author-X-Name-Last: Ericsson Author-Name: Joel Reneby Author-X-Name-First: Joel Author-X-Name-Last: Reneby Title: Stock options as barrier contingent claims Abstract: A comprehensive model is suggested that values securities as options and consequently ordinary stock options as compound options. Extending the basic Black-Scholes model, it can incorporate common contractual features and stylized facts. More specifically, a closed form solution is derived for the price of a call option on a down-and-out call. It is then shown how the result obtained can be generalized in order to price options on complex corporate securities, allowing among other things for corporate taxation, costly financial distress and deviations from the absolute priority rule. The characteristics of the model are illustrated with numerical examples. Journal: Applied Mathematical Finance Pages: 121-147 Issue: 2 Volume: 10 Year: 2003 Keywords: model, stock options, corporate securities, X-DOI: 10.1080/1350486032000088921 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000088921 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:2:p:121-147 Template-Type: ReDIF-Article 1.0 Author-Name: Juri Hinz Author-X-Name-First: Juri Author-X-Name-Last: Hinz Title: Modelling day-ahead electricity prices Abstract: A production-based approach is introduced to take into account different attitudes and liabilities of market participants to discuss the equilibrium day-ahead prices on electricity. Conditions ensuring the existence of the equilibrium are given and price distribution is considered. A discussion of reasons for high price volatility is given. Journal: Applied Mathematical Finance Pages: 149-161 Issue: 2 Volume: 10 Year: 2003 Keywords: day-ahead electricity prices, equilibrium pricing, X-DOI: 10.1080/1350486032000130329 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000130329 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:2:p:149-161 Template-Type: ReDIF-Article 1.0 Author-Name: Yumiharu Nakano Author-X-Name-First: Yumiharu Author-X-Name-Last: Nakano Title: Minimizing coherent risk measures of shortfall in discrete-time models with cone constraints Abstract: The paper studies the problem of minimizing coherent risk measures of shortfall for general discrete-time financial models with cone-constrained trading strategies, as developed by Pham and Touzi. It is shown that the optimal strategy is obtained by super-hedging a contingent claim, which is represented as a Neyman-Pearson-type random variable. Journal: Applied Mathematical Finance Pages: 163-181 Issue: 2 Volume: 10 Year: 2003 Keywords: coherent risk measure, shortfall risk, constrained strategy, super-hedging, convex duality, X-DOI: 10.1080/1350486032000102924 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000102924 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:2:p:163-181 Template-Type: ReDIF-Article 1.0 Author-Name: A. D'Aspremont Author-X-Name-First: A. Author-X-Name-Last: D'Aspremont Title: Interest rate model calibration using semidefinite Programming Abstract: It is shown that, for the purpose of pricing swaptions, the swap rate and the corresponding forward rates can be considered lognormal under a single martingale measure. Swaptions can then be priced as options on a basket of lognormal assets and an approximation formula is derived for such options. This formula is centred around a Black-Scholes price with an appropriate volatility, plus a correction term that can be interpreted as the expected tracking error. The calibration problem can then be solved very efficiently using semidefinite programming. Journal: Applied Mathematical Finance Pages: 183-213 Issue: 3 Volume: 10 Year: 2003 Keywords: semidefinite programming, Libor market model, calibration, basket options, X-DOI: 10.1080/1350486032000141002 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000141002 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:3:p:183-213 Template-Type: ReDIF-Article 1.0 Author-Name: Jorg Kampen Author-X-Name-First: Jorg Author-X-Name-Last: Kampen Author-Name: Marco Avellaneda Author-X-Name-First: Marco Author-X-Name-Last: Avellaneda Title: On parabolic equations with gauge function term and applications to the multidimensional Leland equation Abstract: Sufficient conditions for existence and a closed form probabilistic representation are obtained for solutions of nonlinear parabolic equations with gauge function term. In particular, the result applies to the generalized Leland equationwhere BSn is the n-dimensional Black-Scholes operator, Ai are positive transaction cost numbers, ρjk are the correlations between returns of asset Sj and asset Sk and DSrkV is an abbreviation of along with the volatilities σr of the rth asset Sr. It is shown that the associated Cauchy problem has a solution for uniformily bounded continuous data if for all i, j, i≠j 0≤Ai<1 and [image omitted] [image omitted]Comment is made on the existence, as Ai→1 for some i, of small and large correlations between returns of assets. Journal: Applied Mathematical Finance Pages: 215-228 Issue: 3 Volume: 10 Year: 2003 X-DOI: 10.1080/1350486032000107361 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000107361 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:3:p:215-228 Template-Type: ReDIF-Article 1.0 Author-Name: Steven Li Author-X-Name-First: Steven Author-X-Name-Last: Li Title: A valuation model for firms with stochastic earnings Abstract: A model is proposed to value a firm with stochastic earnings. It is assumed that the earnings of the firm follow a time-varying mean reverting stochastic process. It is shown that the value of the firm satisfies a boundary value problem of a second-order partial differential equation, which can be solved numerically. Some special cases are discussed. An analytic solution is found for one special case. Moreover, it is shown that the analytic solution is consistent with a previous result obtained by other researchers. Numerical solutions are obtained for the other special cases. Finally, the model is also applied to value the debt issued by the firm. Journal: Applied Mathematical Finance Pages: 229-243 Issue: 3 Volume: 10 Year: 2003 Keywords: stochastic earnings, firm valuation, debt valuation, X-DOI: 10.1080/1350486032000148311 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000148311 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:3:p:229-243 Template-Type: ReDIF-Article 1.0 Author-Name: Hoi Ying Wong Author-X-Name-First: Hoi Ying Author-X-Name-Last: Wong Author-Name: Yue-Kuen Kwok Author-X-Name-First: Yue-Kuen Author-X-Name-Last: Kwok Title: Multi-asset barrier options and occupation time derivatives Abstract: A general framework is formulated to price various forms of European style multi-asset barrier options and occupation time derivatives with one state variable having the barrier feature. Based on the lognormal assumption of asset price processes, the splitting direction technique is developed for deriving the joint density functions of multi-variate terminal asset prices with provision for single or double barriers on one of the state variables. A systematic procedure is illustrated whereby multi-asset option price formulas can be deduced in a systematic manner as extensions from those of their one-asset counterparts. The formulation has been applied successfully to derive the analytic price formulas of multi-asset options with external two-sided barriers and sequential barriers, multi-asset step options and delayed barrier options. The successful numerical implementation of these price formulas is demonstrated. Journal: Applied Mathematical Finance Pages: 245-266 Issue: 3 Volume: 10 Year: 2003 Keywords: multi-asset barrier options, occupation time derivatives, splitting direction technique, X-DOI: 10.1080/1350486032000107352 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000107352 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:3:p:245-266 Template-Type: ReDIF-Article 1.0 Author-Name: C. Atkinson Author-X-Name-First: C. Author-X-Name-Last: Atkinson Author-Name: S. Mokkhavesa Author-X-Name-First: S. Author-X-Name-Last: Mokkhavesa Title: Intertemporal portfolio optimization with small transaction costs and stochastic variance Abstract: The solution to the intertemporal optimal portfolio selection and consumption rule with small transaction costs is derived via the use of perturbation analysis for the two assets portfolio, one risky and one riskfree. This methodology allows us to apply a broader specification for the function of utility. The additional feature of stochastic variance is also included. Journal: Applied Mathematical Finance Pages: 267-302 Issue: 4 Volume: 10 Year: 2003 X-DOI: 10.1080/1350486032000141011 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000141011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:4:p:267-302 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Title: On arbitrage-free pricing of weather derivatives based on fractional Brownian motion Abstract: We derive an arbitrage-free pricing dynamics for claims on temperature, where the temperature follows a fractional Ornstein-Uhlenbeck process. Using a fractional white noise calculus, one can express the dynamics as a special type of conditional expectation not coinciding with the classical one. Using a Fourier transformation technique, explicit expressions are derived for claims of European and average type, and it is shown that these pricing formulas are solutions of certain Black and Scholes partial differential equations. Our results partly confirm a conjecture made by Brody, Syroka and Zervos. Journal: Applied Mathematical Finance Pages: 303-324 Issue: 4 Volume: 10 Year: 2003 Keywords: Fractional Brownian motion, weather derivatives, arbitrage, option pricing, partial-differential equations, white noise analysis, X-DOI: 10.1080/1350486032000174628 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000174628 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:4:p:303-324 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Author-Name: Lars Ekeland Author-X-Name-First: Lars Author-X-Name-Last: Ekeland Author-Name: Ragnar Hauge Author-X-Name-First: Ragnar Author-X-Name-Last: Hauge Author-Name: BjøRn Fredrik Nielsen Author-X-Name-First: BjøRn Fredrik Author-X-Name-Last: Nielsen Title: A note on arbitrage-free pricing of forward contracts in energy markets Abstract: Arbitrage theory is used to price forward (futures) contracts in energy markets, where the underlying assets are non-tradeable. The method is based on the so-called 'fitting of the yield curve' technique from interest rate theory. The spot price dynamics of Schwartz is generalized to multidimensional correlated stochastic processes with Wiener and Levy noise. Findings are illustrated with examples from oil and electricity markets. Journal: Applied Mathematical Finance Pages: 325-336 Issue: 4 Volume: 10 Year: 2003 Keywords: incomplete markets, forward pricing, energy markets, no-arbitrage pricing, Levy processes, X-DOI: 10.1080/1350486032000160777 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000160777 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:4:p:325-336 Template-Type: ReDIF-Article 1.0 Author-Name: Andre Lucas Author-X-Name-First: Andre Author-X-Name-Last: Lucas Author-Name: Pieter Klaassen Author-X-Name-First: Pieter Author-X-Name-Last: Klaassen Author-Name: Peter Spreij Author-X-Name-First: Peter Author-X-Name-Last: Spreij Author-Name: Stefan Straetmans Author-X-Name-First: Stefan Author-X-Name-Last: Straetmans Title: Tail behaviour of credit loss distributions for general latent factor models Abstract: Using a limiting approach to portfolio credit risk, we obtain analytic expressions for the tail behavior of credit losses. To capture the co-movements in defaults over time, we assume that defaults are triggered by a general, possibly non-linear, factor model involving both systematic and idiosyncratic risk factors. The model encompasses default mechanisms in popular models of portfolio credit risk, such as CreditMetrics and CreditRisk+. We show how the tail characteristics of portfolio credit losses depend directly upon the factor model's functional form and the tail properties of the model's risk factors. In many cases the credit loss distribution has a polynomial (rather than exponential) tail. This feature is robust to changes in tail characteristics of the underlying risk factors. Finally, we show that the interaction between portfolio quality and credit loss tail behavior is strikingly different between the CreditMetrics and CreditRisk+ approach to modeling portfolio credit risk. Journal: Applied Mathematical Finance Pages: 337-357 Issue: 4 Volume: 10 Year: 2003 Keywords: portfolio credit risk, extreme value theory, tail events, tail index, factor models, economic capital, portfolio quality, second-order expansions, X-DOI: 10.1080/1350486032000160786 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486032000160786 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:10:y:2003:i:4:p:337-357 Template-Type: ReDIF-Article 1.0 Author-Name: Ales Cerny Author-X-Name-First: Ales Author-X-Name-Last: Cerny Title: Dynamic programming and mean-variance hedging in discrete time Abstract: In this paper the general discrete time mean-variance hedging problem is solved by dynamic programming. Thanks to its simple recursive structure the solution is well suited to computer implementation. On the theoretical side, it is shown how the variance-optimal measure arises in the dynamic programming solution and how one can define conditional expectations under this (generally non-equivalent) measure. The result is then related to the results of previous studies in continuous time. Journal: Applied Mathematical Finance Pages: 1-25 Issue: 1 Volume: 11 Year: 2004 Keywords: mean-variance hedging, discrete time, dynamic programming, incomplete market, arbitrage, X-DOI: 10.1080/1350486042000196164 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000196164 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:1:p:1-25 Template-Type: ReDIF-Article 1.0 Author-Name: Josep Perello Author-X-Name-First: Josep Author-X-Name-Last: Perello Author-Name: Jaume Masoliver Author-X-Name-First: Jaume Author-X-Name-Last: Masoliver Author-Name: Jean-Philippe Bouchaud Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Bouchaud Title: Multiple time scales in volatility and leverage correlations: a stochastic volatility model Abstract: Financial time series exhibit two different type of non-linear correlations: (i) volatility autocorrelations that have a very long-range memory, on the order of years, and (ii) asymmetric return-volatility (or 'leverage') correlations that are much shorter ranged. Different stochastic volatility models have been proposed in the past to account for both these correlations. However, in these models, the decay of the correlations is exponential, with a single time scale for both the volatility and the leverage correlations, at variance with observations. This paper extends the linear Ornstein-Uhlenbeck stochastic volatility model by assuming that the mean reverting level is itself random. It is found that the resulting three-dimensional diffusion process can account for different correlation time scales. It is shown that the results are in good agreement with a century of the Dow Jones index daily returns (1900-2000), with the exception of crash days. Journal: Applied Mathematical Finance Pages: 27-50 Issue: 1 Volume: 11 Year: 2004 X-DOI: 10.1080/1350486042000196155 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000196155 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:1:p:27-50 Template-Type: ReDIF-Article 1.0 Author-Name: C. Tsibiridi Author-X-Name-First: C. Author-X-Name-Last: Tsibiridi Author-Name: C. Atkinson Author-X-Name-First: C. Author-X-Name-Last: Atkinson Title: A possible way of estimating options with stable distributed underlying asset prices Abstract: Option pricing theory is considered when the underlying asset price satisfies a stochastic differential equation which is driven by random motions generated by stable distributions. The properties of the stable distributions are discussed and their connection with the theory of fractional Brownian motion is noted. This approach attempts to generalize the classical Black-Scholes formulation, to allow for the presence of fat tails in the distribution of log prices which leads to a diffusion equation involving fractional Brownian motion. The resulting option pricing via a hedging strategy approach is independently derived by constructing a backward Kolmogorov equation for a simple trinomial model where the probabilities are assumed to satisfy a particular fractional Taylor series due to Dzherbashyan and Nersesyan. To effect this development, some knowledge of fractional integration and differentiation is required so this is briefly reviewed. Consideration is also given to a different hedging strategy approach leading to a fractional Black-Scholes equation involving the market price of risk. Modification to the model is also considered such as the impact of transaction costs. A simple example of American options is also considered. Journal: Applied Mathematical Finance Pages: 51-75 Issue: 1 Volume: 11 Year: 2004 Keywords: stable distributions, fractional Taylor series, fractional Black-Scholes equation, X-DOI: 10.1080/1350486042000190331 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000190331 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:1:p:51-75 Template-Type: ReDIF-Article 1.0 Author-Name: Victor Vaugirard Author-X-Name-First: Victor Author-X-Name-Last: Vaugirard Title: Hitting time and time change Abstract: This paper determines first-passage time distributions with a twofold emphasis on the dynamics of the state variables and interest rate uncertainty. Underlyings follow two-dimensional geometric Brownian motions, Ornstein-Uhlenbeck processes or Poisson jump-diffusion processes, and boundaries are either fixed or indexed on risk-free bonds. Forward-neutral changes of numeraire enable one to derive generic valuation expressions, while changing time allows one to determine closed-form solutions for geometric Brownian motions and moving barriers. In turn, the latter formulas are used to reduce the variance of Monte Carlo simulations in the case of jump-diffusion processes, by means of the control variate method. Journal: Applied Mathematical Finance Pages: 77-94 Issue: 1 Volume: 11 Year: 2004 Keywords: digital option, soft barrier, forward-neutral measure, time change, jump-diffusion process, X-DOI: 10.1080/1350486042000190340 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000190340 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:1:p:77-94 Template-Type: ReDIF-Article 1.0 Author-Name: C. Atkinson Author-X-Name-First: C. Author-X-Name-Last: Atkinson Author-Name: S. Mokkhavesa Author-X-Name-First: S. Author-X-Name-Last: Mokkhavesa Title: Multi-asset portfolio optimization with transaction cost Abstract: The inclusion of transaction costs in the optimal portfolio selection and consumption rule problem is accomplished via the use of perturbation analyses. The portfolio under consideration consists of more than one risky asset, which makes numerical methods impractical. The objective is to establish both the transaction and the no-transaction regions that characterize the optimal investment strategy. The optimal transaction boundaries for two and three risky assets portfolios are solved explicitly. A procedure for solving the N risky assets portfolio is described. The formulation used also reduces the restriction on the functional form of the utility preference. Journal: Applied Mathematical Finance Pages: 95-123 Issue: 2 Volume: 11 Year: 2004 X-DOI: 10.1080/13504860410001693496 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860410001693496 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:2:p:95-123 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Bee Author-X-Name-First: Marco Author-X-Name-Last: Bee Title: Modelling credit default swap spreads by means of normal mixtures and copulas Abstract: This paper develops a multivariate statistical model for the analysis of credit default swap spreads. Given the large excess kurtosis of the univariate marginal distributions, it is proposed to model them by means of a mixture of distributions. However, the multivariate extension of this methodology is numerically difficult, so that copulas are used to capture the structure of dependence of the data. It is shown how to estimate the parameters of the marginal distributions via the EM algorithm; then the parameters of the copula are estimated and standard errors computed through the nonparametric bootstrap. An application to credit default swap spreads of some European reference entities and extensive simulation results confirm the effectiveness of the method. Journal: Applied Mathematical Finance Pages: 125-146 Issue: 2 Volume: 11 Year: 2004 Keywords: finite mixture distributions, copula, credit default swap spread, non-parametric bootstrap, X-DOI: 10.1080/1350486042000218420 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000218420 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:2:p:125-146 Template-Type: ReDIF-Article 1.0 Author-Name: Joanna Goard Author-X-Name-First: Joanna Author-X-Name-Last: Goard Author-Name: Noel Hansen Author-X-Name-First: Noel Author-X-Name-Last: Hansen Title: Comparison of the performance of a time-dependent short-interest rate model with time-independent models Abstract: The coefficients in the stochastic differential equation that the short interest rate follows are of vital importance in the subsequent modelling of bond prices and other interest rate products. Empirical tests have previously been performed by various authors who compare a variety of popular short-rate models. Most recently, Ahn and Gao compared their model with affine-drift models and showed that their model with a non-linear drift function outperforms the others. This paper compares the model developed by Goard, which is a time-dependent generalization of the Ahn-Gao model, with the Ahn-Gao model itself. It is found that the time-dependent model using a second-order Fourier series in time, outperforms the Ahn-Gao model for all data sets considered. Journal: Applied Mathematical Finance Pages: 147-164 Issue: 2 Volume: 11 Year: 2004 Keywords: short-rate, interest rate models, X-DOI: 10.1080/13504860410001686034 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860410001686034 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:2:p:147-164 Template-Type: ReDIF-Article 1.0 Author-Name: Wing Hoe Woo Author-X-Name-First: Wing Hoe Author-X-Name-Last: Woo Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Title: A dynamic binomial expansion technique for credit risk measurement: a Bayesian filtering approach Abstract: Credit risk measurement and management are important and current issues in the modern finance world from both the theoretical and practical perspectives. There are two major schools of thought for credit risk analysis, namely the structural models based on the asset value model originally proposed by Merton and the intensity-based reduced form models. One of the popular credit risk models used in practice is the Binomial Expansion Technique (BET) introduced by Moody's. However, its one-period static nature and the independence assumption for credit entities' defaults are two shortcomings for the use of BET in practical situations. Davis and Lo provided elegant ways to ease the two shortcomings of BET with their default infection and dynamic continuous-time intensity-based approaches. This paper first proposes a discrete-time dynamic extension to the BET in order to incorporate the time-dependent and time-varying behaviour of default probabilities for measuring the risk of a credit risky portfolio. In reality, the 'true' default probabilities are unobservable to credit analysts and traders. Here, the uncertainties of 'true' default probabilities are incorporated in the context of a dynamic Bayesian paradigm. Numerical studies of the proposed model are provided. Journal: Applied Mathematical Finance Pages: 165-186 Issue: 2 Volume: 11 Year: 2004 Keywords: credit risk measurement, binomial expansion technique (BET), default probabilities, Bayesian filtering method, value at risk (VaR), X-DOI: 10.1080/13504860410001682669 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860410001682669 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:2:p:165-186 Template-Type: ReDIF-Article 1.0 Author-Name: Senay Ağca Author-X-Name-First: Senay Author-X-Name-Last: Ağca Author-Name: Don Chance Author-X-Name-First: Don Author-X-Name-Last: Chance Title: Two extensions for fitting discrete time term structure models with normally distributed factors Abstract: This paper provides extensions to procedures for the implementation of two well-known term structure models. In the first part, a misleading implication given in two textbooks concerning the ability to fit a Ho-Lee type term structure tree through trial and error is corrected, and it is shown that the tree can be fitted precisely with a simple and easily programmable formula. In the second part, a previously published result that obtains the drift for a single-factor discrete time Heath-Jarrow-Morton model is extended to a multi-factor world. In both cases numerical examples are provided. Journal: Applied Mathematical Finance Pages: 187-205 Issue: 3 Volume: 11 Year: 2004 Keywords: term structure, Ho-Lee model, Heath-Jarrow-Morton model, X-DOI: 10.1080/1350486042000228717 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000228717 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:3:p:187-205 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Chesney Author-X-Name-First: Marc Author-X-Name-Last: Chesney Author-Name: M. Jeanblanc Author-X-Name-First: M. Author-X-Name-Last: Jeanblanc Title: Pricing American currency options in an exponential Levy model Abstract: In this article the problem of the American option valuation in a Levy process setting is analysed. The perpetual case is first considered. Without possible discontinuities (i.e. with negative jumps in the call case), known results concerning the currency option value as well as the exercise boundary are obtained with a martingale approach. With possible discontinuities of the underlying process at the exercise boundary (i.e. with positive jumps in the call case), original results are derived by relying on first passage time and overshoot associated with a Levy process. For finite life American currency calls, the formula derived by Bates or Zhang, in the context of a negative jump size, is tested. It is basically an extension of the one developed by Mac Millan and extended by Barone-Adesi and Whaley. It is shown that Bates' model generates pretty good results only when the process is continuous at the exercise boundary. Journal: Applied Mathematical Finance Pages: 207-225 Issue: 3 Volume: 11 Year: 2004 Keywords: American options, perpetual options, exercise boundary, incomplete markets, jump diffusion model, Laplace transform, stopping times, Levy exponent, overshoot, X-DOI: 10.1080/1350486042000249336 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000249336 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:3:p:207-225 Template-Type: ReDIF-Article 1.0 Author-Name: C. Johnson Author-X-Name-First: C. Author-X-Name-Last: Johnson Author-Name: Y. Omar Author-X-Name-First: Y. Author-X-Name-Last: Omar Author-Name: P. Ouwehand Author-X-Name-First: P. Author-X-Name-Last: Ouwehand Title: Valuing risky income streams in incomplete markets Abstract: A model for pricing and hedging in incomplete markets is proposed. This model is derived from expected utility theory, and a connection with the traditional no-arbitrage framework is noted. It is shown that the CGM model can be implemented to value risky assets in incomplete markets. Journal: Applied Mathematical Finance Pages: 227-258 Issue: 3 Volume: 11 Year: 2004 Keywords: pricing in incomplete markets, expected utility, coherent risk measures, X-DOI: 10.1080/1350486042000228726 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000228726 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:3:p:227-258 Template-Type: ReDIF-Article 1.0 Author-Name: Alessio Sancetta Author-X-Name-First: Alessio Author-X-Name-Last: Sancetta Author-Name: Steve Satchell Author-X-Name-First: Steve Author-X-Name-Last: Satchell Title: Calculating hedge fund risk: the draw down and the maximum draw down Abstract: Hedge funds, defined in this context as geared financial entities, frequently use some measure of point loss as a risk measure. This paper considers the statistical properties of an uninterrupted fall in a security price; called a draw down. The distribution of the draw downs in an N-trading period is derived together with an approximation to the distribution of the maximum. Complementary results are provided which are useful for risk calculations. A brief empirical study of the S&P futures is included in order to highlight some of the limitations in the presence of extreme events. Journal: Applied Mathematical Finance Pages: 259-282 Issue: 3 Volume: 11 Year: 2004 Keywords: Characteristic function, Downside risk, KST distribution, X-DOI: 10.1080/1350486042000220553 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000220553 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:3:p:259-282 Template-Type: ReDIF-Article 1.0 Author-Name: Pedro Gutierrez Author-X-Name-First: Pedro Author-X-Name-Last: Gutierrez Title: Money, prices and interest rates in a non-aggregate stochastic general equilibrium model Abstract: This paper explores the relationships between money, prices, uncertainty and interest rates in a stochastic general equilibrium model. Taking a non-aggregate pure exchange economy with time and uncertainty as the starting point, money is introduced as a means to keep track of past transactions of goods and insurance services and as an instrument to settle debts. As a result, in this stochastic general equilibrium model the desire to hold money arises from the demand of goods and services, Arrow-Debreu securities, and assets. Since these sources of demand for money are strongly related to the economy output, the economy degree of uncertainty, and the interest rates, this paper provides not only an alternative framework to the traditional keynesian analysis of the liquidity preference, but also an extension of the cash-in-advance models for introducing money in a general equilibrium model. Journal: Applied Mathematical Finance Pages: 283-316 Issue: 4 Volume: 11 Year: 2004 Keywords: stochastic general equilibrium, demand for money, cash-in-advance model, X-DOI: 10.1080/13504860420000231911 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860420000231911 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:4:p:283-316 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Howison Author-X-Name-First: Sam Author-X-Name-Last: Howison Author-Name: Avraam Rafailidis Author-X-Name-First: Avraam Author-X-Name-Last: Rafailidis Author-Name: Henrik Rasmussen Author-X-Name-First: Henrik Author-X-Name-Last: Rasmussen Title: On the pricing and hedging of volatility derivatives Abstract: The paper considers the pricing of a range of volatility derivatives, including volatility and variance swaps and swaptions. Under risk-neutral valuation closed-form formulae for volatility-average and variance swaps for a variety of diffusion and jump-diffusion models for volatility are provided. A general partial differential equation framework for derivatives that have an extra dependence on an average of the volatility is described. Approximate solutions of this equation are given for volatility products written on assets for which the volatility process fluctuates on a timescale that is fast compared with the lifetime of the contracts, analysing both the 'outer' region and, by matched asymptotic expansions, the 'inner' boundary layer near expiry. Journal: Applied Mathematical Finance Pages: 317-346 Issue: 4 Volume: 11 Year: 2004 X-DOI: 10.1080/1350486042000254024 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000254024 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:4:p:317-346 Template-Type: ReDIF-Article 1.0 Author-Name: Stoyan Valchev Author-X-Name-First: Stoyan Author-X-Name-Last: Valchev Title: Stochastic volatility Gaussian Heath-Jarrow-Morton models Abstract: This paper extends the class of deterministic volatility Heath-Jarrow-Morton models to a Markov chain stochastic volatility framework allowing for jump discontinuities and a variety of deformations of the term structure of forward rate volatilities. Analytical solutions for the dynamics of the volatility term structure are obtained. Semimartingale decompositions of the interest rates under a spot and forward martingale measures are identified. Stochastic volatility versions of the continuous time Ho-Lee and Hull-White extended Vasicek models are obtained. Introducing a regime shift in volatility that is an exponential function of time to maturity leads to a Vasicek dynamics with regime switching coefficients of the short rate. Journal: Applied Mathematical Finance Pages: 347-368 Issue: 4 Volume: 11 Year: 2004 Keywords: term structure of interest rates, Heath-Jarrow-Morton model, stochastic volatility, continuous time Markov chains, piecewise-deterministic Markov processes, X-DOI: 10.1080/1350486042000231902 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000231902 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:11:y:2004:i:4:p:347-368 Template-Type: ReDIF-Article 1.0 Author-Name: Enrique Ballestero Author-X-Name-First: Enrique Author-X-Name-Last: Ballestero Title: Mean-Semivariance Efficient Frontier: A Downside Risk Model for Portfolio Selection Abstract: An ongoing stream in financial analysis proposes mean-semivariance in place of mean-variance as an alternative approach to portfolio selection, since segments of investors are more averse to returns below the mean value than to deviations above and below the mean value. Accordingly, this paper searches for a stochastic programming model in which the portfolio semivariance is the objective function to be minimized subject to standard parametric constraints, which leads to the mean-semivariance efficient frontier. The proposed model relies on an empirically tested basis, say, portfolio diversification and the empirical validity of Sharpe's beta regression equation relating each asset return to the market. From this basis, the portfolio semivariance matrix form is strictly mathematically derived, thus an operational quadratic objective function is obtained without resorting to heuristics. Ease of computation is highlighted by a numerical example, which allows one to compare the results from the proposed mean-semivariance approach with those derived from the traditional mean-variance model. Journal: Applied Mathematical Finance Pages: 1-15 Issue: 1 Volume: 12 Year: 2005 Keywords: Covariance matrix, downside risk, parametric quadratic programming, portfolio semivariance, risk measures, X-DOI: 10.1080/1350486042000254015 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000254015 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:1-15 Template-Type: ReDIF-Article 1.0 Author-Name: Carl Chiarella Author-X-Name-First: Carl Author-X-Name-Last: Chiarella Author-Name: Roberto Dieci Author-X-Name-First: Roberto Author-X-Name-Last: Dieci Author-Name: Laura Gardini Author-X-Name-First: Laura Author-X-Name-Last: Gardini Title: The Dynamic Interaction of Speculation and Diversification Abstract: A discrete time model of a financial market is developed, in which heterogeneous interacting groups of agents allocate their wealth between two risky assets and a riskless asset. In each period each group formulates its demand for the risky assets and the risk-free asset according to myopic mean-variance maximizazion. The market consists of two types of agents: fundamentalists, who hold an estimate of the fundamental values of the risky assets and whose demand for each asset is a function of the deviation of the current price from the fundamental, and chartists, a group basing their trading decisions on an analysis of past returns. The time evolution of the prices is modelled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an offsetting long or short position, and who announces the next period prices as functions of the excess demand for each asset and with a view to long-run market stability. The model is reduced to a seven-dimensional nonlinear discrete-time dynamical system, that describes the time evolution of prices and agents' beliefs about expected returns, variances and correlation. The unique steady state of the model is determined and the local asymptotic stability of the equilibrium is analysed, as a function of the key parameters that characterize agents' behaviour. In particular it is shown that when chartists update their expectations sufficiently fast, then the stability of the equilibrium is lost through a supercritical Neimark-Hopf bifurcation, and self-sustained price fluctuations along an attracting limit cycle appear in one or both markets. Global analysis is also performed, by using numerical techniques, in order to understand the role played by the chartists' behaviour in the transition to a regime characterized by irregular oscillatory motion and coexistence of attractors. It is also shown how changes occurring in one market may affect the price dynamics of the alternative risky asset, as a consequence of the dynamic updating of agents' portfolios. Journal: Applied Mathematical Finance Pages: 17-52 Issue: 1 Volume: 12 Year: 2005 X-DOI: 10.1080/1350486042000260072 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000260072 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:17-52 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Author-Name: Jurate Saltyte-Benth Author-X-Name-First: Jurate Author-X-Name-Last: Saltyte-Benth Title: Stochastic Modelling of Temperature Variations with a View Towards Weather Derivatives Abstract: Daily average temperature variations are modelled with a mean-reverting Ornstein-Uhlenbeck process driven by a generalized hyperbolic Levy process and having seasonal mean and volatility. It is empirically demonstrated that the proposed dynamics fits Norwegian temperature data quite successfully, and in particular explains the seasonality, heavy tails and skewness observed in the data. The stability of mean-reversion and the question of fractionality of the temperature data are discussed. The model is applied to derive explicit prices for some standardized futures contracts based on temperature indices and options on these traded on the Chicago Mercantile Exchange (CME). Journal: Applied Mathematical Finance Pages: 53-85 Issue: 1 Volume: 12 Year: 2005 Keywords: Temperature modelling, stochastic processes, Levy processes, mean-reversion, seasonality, fractionality, temperature futures and options, X-DOI: 10.1080/1350486042000271638 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000271638 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:53-85 Template-Type: ReDIF-Article 1.0 Author-Name: John Knight Author-X-Name-First: John Author-X-Name-Last: Knight Author-Name: Stephen Satchell Author-X-Name-First: Stephen Author-X-Name-Last: Satchell Title: A Re-Examination of Sharpe's Ratio for Log-Normal Prices Abstract: The purpose of this paper is to examine the exact properties of Sharpe's ratio when prices are log-normal. Depending on the definition of returns, different expressions are formed for unbiased estimators of Sharpe's ratio. Journal: Applied Mathematical Finance Pages: 87-100 Issue: 1 Volume: 12 Year: 2005 Keywords: Sharpe's ratio, log-normal prices, unbiased estimation, X-DOI: 10.1080/1350486042000271647 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000271647 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:1:p:87-100 Template-Type: ReDIF-Article 1.0 Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Author-Name: Li Chen Author-X-Name-First: Li Author-X-Name-Last: Chen Author-Name: H. Vincent Poor Author-X-Name-First: H. Vincent Author-X-Name-Last: Poor Title: Consistency Problems for Jump-diffusion Models Abstract: In this paper consistency problems for multi-factor jump-diffusion models, where the jump parts follow multivariate point processes are examined. First the gap between jump-diffusion models and generalized Heath-Jarrow-Morton (HJM) models is bridged. By applying the drift condition for a generalized arbitrage-free HJM model, the consistency condition for jump-diffusion models is derived. Then a cause is considered in which the forward rate curve has a separable structure, and a specific version of the general consistency condition is obtained. In particular, a necessary and sufficient condition for a jump-diffusion model to be affine is provided. Finally the Nelson-Siegel type of forward curve structures is discussed. It is demonstrated that under regularity condition, there exists no jump-diffusion model consistent with the Nelson-Siegel curves. Journal: Applied Mathematical Finance Pages: 101-119 Issue: 2 Volume: 12 Year: 2005 Keywords: Interest rate models, consistency problems, jump diffusion models, Nelson-Siegel curves, X-DOI: 10.1080/1350486042000297234 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000297234 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:2:p:101-119 Template-Type: ReDIF-Article 1.0 Author-Name: San-Lin Chung Author-X-Name-First: San-Lin Author-X-Name-Last: Chung Author-Name: Hsiao-Fen Yang Author-X-Name-First: Hsiao-Fen Author-X-Name-Last: Yang Title: Pricing Quanto Equity Swaps in a Stochastic Interest Rate Economy Abstract: This paper derives a pricing model for a quanto foreign equity/domestic floating rate swap in which one party pays domestic floating interest rates and receives foreign stock returns determined in the foreign currency, but is paid in the domestic currency. We use the risk-neutral valuation technique developed by Amin and Bodurtha to generate an arbitrage-free pricing model. A closed-form solution is obtained under further restrictions on the drift rates of the asset price processes. Pricing formulae show that the value of a quanto equity swap at the start date does not depend on the foreign stock price level, but rather on the term structures of both countries and other parameters. However, the foreign stock price levels do affect the swap value times between two payment dates. The numerical implementations indicate that the domestic and foreign term structures, the correlation between the foreign interest rate and the exchange rate, and the correlation between the exchange rate and the foreign stock are more important factors in pricing a quanto equity swap than other correlations. Journal: Applied Mathematical Finance Pages: 121-146 Issue: 2 Volume: 12 Year: 2005 Keywords: Equity swaps, term structure of interest rates, risk-neutral valuation, arbitrage-free pricing model, X-DOI: 10.1080/1350486042000297261 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000297261 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:2:p:121-146 Template-Type: ReDIF-Article 1.0 Author-Name: Vladimir Piterbarg Author-X-Name-First: Vladimir Author-X-Name-Last: Piterbarg Title: Stochastic Volatility Model with Time-dependent Skew Abstract: A formula is derived for the 'effective' skew in a stochastic volatility model with a time-dependent local volatility function. The formula relates the total amount of skew generated by the model over a given time period to the time-dependent slope of the instantaneous local volatility function. A new 'effective' volatility approximation is also derived. The utility of the formulas is demonstrated by building a forward Libor model that can be calibrated to swaption smiles that vary across the swaption grid. Journal: Applied Mathematical Finance Pages: 147-185 Issue: 2 Volume: 12 Year: 2005 Keywords: Stochastic volatility, volatility smile, time-dependent local volatility, effective volatility, effective skew, average skew, homogenization, averaging principle, effective media, forward Libor model, Libor market model, LMM, BGM, volatility calibration, skew calibration, X-DOI: 10.1080/1350486042000297225 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000297225 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:2:p:147-185 Template-Type: ReDIF-Article 1.0 Author-Name: Maria Elvira Mancino Author-X-Name-First: Maria Elvira Author-X-Name-Last: Mancino Author-Name: Roberto Reno Author-X-Name-First: Roberto Author-X-Name-Last: Reno Title: Dynamic Principal Component Analysis of Multivariate Volatility via Fourier Analysis Abstract: A method is proposed to compute a time-varying correlation matrix between asset prices. The method has a natural geometric interpretation in terms of dynamic principal components analysis. The paper illustrates, via Monte Carlo experiments and data analysis, the potential of the method in computing cross-correlations; and it describes market integration, introducing the concept of reference asset. Journal: Applied Mathematical Finance Pages: 187-199 Issue: 2 Volume: 12 Year: 2005 Keywords: Cross-volatilities, Fourier series, dynamic principal component analysis, X-DOI: 10.1080/1350486042000255861 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000255861 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:2:p:187-199 Template-Type: ReDIF-Article 1.0 Author-Name: Yves Achdou Author-X-Name-First: Yves Author-X-Name-Last: Achdou Author-Name: Olivier Pironneau Author-X-Name-First: Olivier Author-X-Name-Last: Pironneau Title: Numerical Procedure for Calibration of Volatility with American Options Abstract: In finance, the price of an American option is obtained from the price of the underlying asset by solving a parabolic variational inequality. The calibration of volatility from the prices of a family of American options yields an inverse problem involving the solution of the previously mentioned parabolic variational inequality. In this paper, the discretization of the variational inequality by finite elements is studied in detail. Then, a calibration procedure, where the volatility belongs to a finite-dimensional space (finite element or bicubic splines) is described. A least square method, with suitable regularization terms is used. Necessary optimality conditions involving adjoint states are given and the differentiability of the cost function is studied. A parallel algorithm is proposed and numerical experiments, on both academic and realistic cases, are presented. Journal: Applied Mathematical Finance Pages: 201-241 Issue: 3 Volume: 12 Year: 2005 Keywords: American options, calibration of local volatility, Least Square Method, optimality conditions, X-DOI: 10.1080/1350486042000297252 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000297252 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:3:p:201-241 Template-Type: ReDIF-Article 1.0 Author-Name: Mattias Jonsson Author-X-Name-First: Mattias Author-X-Name-Last: Jonsson Author-Name: Jan Vecer Author-X-Name-First: Jan Author-X-Name-Last: Vecer Title: Insider Trading in Convergent Markets Abstract: Optimal trading strategies are found for an insider who is trading in two convergent stocks and is bound by margin constraints. Journal: Applied Mathematical Finance Pages: 243-252 Issue: 3 Volume: 12 Year: 2005 Keywords: Convergent stocks, optimal trading strategies, insider, margin constraints, X-DOI: 10.1080/1350486042000325160 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000325160 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:3:p:243-252 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Laurence Author-X-Name-First: Peter Author-X-Name-Last: Laurence Author-Name: Tai-Ho Wang Author-X-Name-First: Tai-Ho Author-X-Name-Last: Wang Title: Sharp Upper and Lower Bounds for Basket Options Abstract: Given a basket option on two or more assets in a one-period static hedging setting, the paper considers the problem of maximizing and minimizing the basket option price subject to the constraints of known option prices on the component stocks and consistency with forward prices and treat it as an optimization problem. Sharp upper bounds are derived for the general n-asset case and sharp lower bounds for the two-asset case, both in closed forms, of the price of the basket option. In the case n = 2 examples are given of discrete distributions attaining the bounds. Hedge ratios are also derived for optimal sub and super replicating portfolios consisting of the options on the individual underlying stocks and the stocks themselves. Journal: Applied Mathematical Finance Pages: 253-282 Issue: 3 Volume: 12 Year: 2005 Keywords: Basket option, duality, sharp bound, X-DOI: 10.1080/1350486042000325179 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000325179 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:3:p:253-282 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Siegl Author-X-Name-First: Thomas Author-X-Name-Last: Siegl Author-Name: Peter Quell Author-X-Name-First: Peter Author-X-Name-Last: Quell Title: Modelling Specific Interest Rate Risk with Estimation of Missing Data Abstract: For the treatment of specific interest rate risk, a risk model is suggested, quantifying and combining both market and credit risk components consistently. The market risk model is based on credit spreads derived from traded bond prices. Though traded bond prices reveal a maximum amount of issuer specific information, illiquidity problems do not allow for classical parameter estimation in this context. To overcome this difficulty an efficient multiple imputation method is proposed that also quantifies the amount of risk associated with missing data. The credit risk component is based on event risk caused by correlated rating migrations of individual bonds using a Copula function approach. Journal: Applied Mathematical Finance Pages: 283-309 Issue: 3 Volume: 12 Year: 2004 Keywords: Statistical estimation with missing data, specific interest rate risk, multiple imputation, EM-algorithm, value at risk, copula functions, X-DOI: 10.1080/1350486042000297243 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486042000297243 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2004:i:3:p:283-309 Template-Type: ReDIF-Article 1.0 Author-Name: Alvaro Cartea Author-X-Name-First: Alvaro Author-X-Name-Last: Cartea Author-Name: Marcelo Figueroa Author-X-Name-First: Marcelo Author-X-Name-Last: Figueroa Title: Pricing in Electricity Markets: A Mean Reverting Jump Diffusion Model with Seasonality Abstract: This paper presents a mean-reverting jump diffusion model for the electricity spot price and derives the corresponding forward price in closed-form. Based on historical spot data and forward data from England and Wales the model is calibrated and months, quarters, and seasons-ahead forward surfaces are presented. Journal: Applied Mathematical Finance Pages: 313-335 Issue: 4 Volume: 12 Year: 2005 Keywords: Energy derivatives, electricity, forward curve, forward surfaces, X-DOI: 10.1080/13504860500117503 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500117503 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:4:p:313-335 Template-Type: ReDIF-Article 1.0 Author-Name: Ingmar Evers Author-X-Name-First: Ingmar Author-X-Name-Last: Evers Title: A Series Solution for Bermudan Options Abstract: This paper presents closed-form expressions for pricing Bermudan options in terms of an infinite series of standard solutions of the Black-Scholes equation. These standard solutions are combined for successive exercise dates using backward induction. At each exercise date, the optimal exercise price of the underlying asset is the root of a one-dimensional nonlinear algebraic equation. Numerical examples demonstrate the convergence of the series to the solution obtained using alternative methods. The work presented precedes a more general approach for Bermudan options on multiple assets involving multi-dimensional Hermite polynomials. Journal: Applied Mathematical Finance Pages: 337-349 Issue: 4 Volume: 12 Year: 2005 Keywords: Bermudan options, Repeated integrals of the error function, Backward induction, Series solution, Multi-asset options, X-DOI: 10.1080/13504860500080263 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500080263 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:4:p:337-349 Template-Type: ReDIF-Article 1.0 Author-Name: Ragnar Norberg Author-X-Name-First: Ragnar Author-X-Name-Last: Norberg Title: Interest Guarantees in Banking Abstract: Interest guarantees on loans and savings contracts are viewed as financial claims and priced by the no arbitrage principle in continuous time Markov interest models of diffusion type and of Markov chain type. Various forms of loan contracts and guarantees are considered, an important distinction being made between loans with fixed repayments and loans with fixed amortizations. Differential equations are obtained for the values of the guarantees, and some closed form expressions are obtained for standard contracts in certain well structured models. Journal: Applied Mathematical Finance Pages: 351-370 Issue: 4 Volume: 12 Year: 2005 Keywords: Stochastic interest, loans, nominal interest rate, diffusion interest model, Markov chain interest model, closed form solutions, X-DOI: 10.1080/13504860500117552 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500117552 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:4:p:351-370 Template-Type: ReDIF-Article 1.0 Author-Name: Graeme West Author-X-Name-First: Graeme Author-X-Name-Last: West Title: Calibration of the SABR Model in Illiquid Markets Abstract: Recently the SABR model has been developed to manage the option smile which is observed in derivatives markets. Typically, calibration of such models is straightforward as there is adequate data available for robust extraction of the parameters required asinputs to the model. The paper considers calibration of the model in situations where input data is very sparse. Although this will require some creative decision making, the algorithms developed here are remarkably robust and can be used confidently for mark to market and hedging of option portfolios. Journal: Applied Mathematical Finance Pages: 371-385 Issue: 4 Volume: 12 Year: 2005 Keywords: SABR model, equity derivatives, volatility skew calibration, illiquid markets, X-DOI: 10.1080/13504860500148672 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500148672 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:12:y:2005:i:4:p:371-385 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Henrard Author-X-Name-First: Marc Author-X-Name-Last: Henrard Title: A Semi-Explicit Approach to Canary Swaptions in HJM One-Factor Model Abstract: Leveraging the explicit formula for European swaptions and coupon-bond options in the HJM one-factor model, a semi-explicit formula for 2-Bermudan options (also called Canary options) is developed. The European swaption formula is extended to future times. So equipped, one is able to reduce the valuation of a 2-Bermudan swaption to a single numerical integration at the first expiry date. In that integration the most complex part of the embedded European swaptions valuation has been simplified to perform it only once and not for every point. In a special but very common in practice case, a semi-explicit formula is provided. Those results lead to a significantly faster and more precise implementation of swaption valuation. The improvements extend even more favourably to sensitivity calculations. Journal: Applied Mathematical Finance Pages: 1-18 Issue: 1 Volume: 13 Year: 2006 Keywords: Bermudan swaption, HJM one-factor model, Hull-White model, explicit formula, numerical integration, X-DOI: 10.1080/13504860500117602 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500117602 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:1-18 Template-Type: ReDIF-Article 1.0 Author-Name: Kevin Fergusson Author-X-Name-First: Kevin Author-X-Name-Last: Fergusson Author-Name: Eckhard Platen Author-X-Name-First: Eckhard Author-X-Name-Last: Platen Title: On the Distributional Characterization of Daily Log-Returns of a World Stock Index Abstract: In this paper distributions are identified which suitably fit log-returns of the world stock index when these are expressed in units of different currencies. By searching for a best fit in the class of symmetric generalized hyperbolic distributions the maximum likelihood estimates appear to cluster in the neighbourhood of those of the Student t distribution. This is confirmed at a high significance level under the likelihood ratio test. Finally, the paper derives the minimal market model, which explains the empirical findings as a consequence of the optimal market dynamics. Journal: Applied Mathematical Finance Pages: 19-38 Issue: 1 Volume: 13 Year: 2006 Keywords: World stock index, log-return distribution, Student t distribution, symmetric generalized hyperbolic distribution, X-DOI: 10.1080/13504860500394052 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500394052 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:19-38 Template-Type: ReDIF-Article 1.0 Author-Name: Leo Krippner Author-X-Name-First: Leo Author-X-Name-Last: Krippner Title: A Theoretically Consistent Version of the Nelson and Siegel Class of Yield Curve Models Abstract: A popular class of yield curve models is based on the Nelson and Siegel approach of 'fitting' yield curve data with simple functions of maturity. However, such models cannot be consistent across time. This article addresses that deficiency by deriving an intertemporally consistent and arbitrage-free version of the Nelson and Siegel model. Adding this theoretical consistency expands the potential applications of the Nelson and Siegel approach to exercises involving a time-series context, such as forecasting the yield curve and pricing interest rate derivatives. As a practical example, the intertemporal consistency of the model is exploited to derive a theoretical framework for forecasting the yield curve. The empirical application of that framework to United States data results in out-of-sample forecasts that outperform the random walk over the sample period of almost 50 years, for forecast horizons ranging from six months to three years. Journal: Applied Mathematical Finance Pages: 39-59 Issue: 1 Volume: 13 Year: 2006 Keywords: Yield curve, term structure of interest rates, Nelson and Siegel model, Heath-Jarrow-Morton framework, X-DOI: 10.1080/13504860500394367 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500394367 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:39-59 Template-Type: ReDIF-Article 1.0 Author-Name: Joel Vanden Author-X-Name-First: Joel Author-X-Name-Last: Vanden Title: Exact Superreplication Strategies for a Class of Derivative Assets Abstract: A superreplicating hedging strategy is commonly used when delta hedging is infeasible or is too expensive. This article provides an exact analytical solution to the superreplication problem for a class of derivative asset payoffs. The class contains common payoffs that are neither uniformly convex nor concave. A digital option, a bull spread, a bear spread, and some portfolios of bull spreads or bear spreads, are all included as special cases. The problem is approached by first solving for the transition density of a process that has a two-valued volatility. Using this process to model the underlying asset and identifying the two volatility values as σmin and σmax, the value function for any derivative asset in the class is shown to solve the Black-Scholes-Barenblatt equation. The subreplication problem and several related extensions, such as option pricing with transaction costs, calculating superreplicating bounds, and superreplication with multiple risky assets, are also addressed. Journal: Applied Mathematical Finance Pages: 61-87 Issue: 1 Volume: 13 Year: 2006 Keywords: Superreplication, subreplication, uncertain volatility, Black-Scholes-Barenblatt equation, transaction costs, X-DOI: 10.1080/13504860500117560 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500117560 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:1:p:61-87 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Hagan Author-X-Name-First: Patrick Author-X-Name-Last: Hagan Author-Name: Graeme West Author-X-Name-First: Graeme Author-X-Name-Last: West Title: Interpolation Methods for Curve Construction Abstract: This paper surveys a wide selection of the interpolation algorithms that are in use in financial markets for construction of curves such as forward curves, basis curves, and most importantly, yield curves. In the case of yield curves the issue of bootstrapping is reviewed and how the interpolation algorithm should be intimately connected to the bootstrap itself is discussed. The criterion for inclusion in this survey is that the method has been implemented by a software vendor (or indeed an inhouse developer) as a viable option for yield curve interpolation. As will be seen, many of these methods suffer from problems: they posit unreasonable expections, or are not even necessarily arbitrage free. Moreover, many methods lead one to derive hedging strategies that are not intuitively reasonable. In the last sections, two new interpolation methods (the monotone convex method and the minimal method) are introduced, which it is believed overcome many of the problems highlighted with the other methods discussed in the earlier sections. Journal: Applied Mathematical Finance Pages: 89-129 Issue: 2 Volume: 13 Year: 2006 Keywords: Yield curve, interpolation, bootstrap, X-DOI: 10.1080/13504860500396032 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500396032 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:2:p:89-129 Template-Type: ReDIF-Article 1.0 Author-Name: Hyejin Ku Author-X-Name-First: Hyejin Author-X-Name-Last: Ku Title: Liquidity Risk with Coherent Risk Measures Abstract: This paper concerns questions related to the regulation of liquidity risk, and proposes a definition of an acceptable portfolio. Because the concern is with risk management, the paper considers processes under the physical (rather than the martingale) measure. Basically, a portfolio is 'acceptable' provided there is a trading strategy (satisfying some limitations on market liquidity) which, at some fixed date in the future, produces a cash-only position, (possibly) having positive future cash flows, which is required to satisfy a 'convex risk measure constraint'. Journal: Applied Mathematical Finance Pages: 131-141 Issue: 2 Volume: 13 Year: 2006 Keywords: Coherent risk measures, liquidity risk, acceptable portfolio, X-DOI: 10.1080/13504860600563143 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600563143 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:2:p:131-141 Template-Type: ReDIF-Article 1.0 Author-Name: Carlo Mari Author-X-Name-First: Carlo Author-X-Name-Last: Mari Author-Name: Roberto Reno Author-X-Name-First: Roberto Author-X-Name-Last: Reno Title: Arbitrary Initial Term Structure within the CIR Model: A Perturbative Solution Abstract: Single-factor interest rate models with constant coefficients are not consistent with arbitrary initial term structures. An extension which allows both arbitrary initial term structure and analytical tractability has been provided only in the Gaussian case. In this paper, within the context of the HJM methodology, an extension of the CIR model is provided which admits arbitrary initial term structure. It is shown how to calculate bond prices via a perturbative approach, and closed formulas are provided at every order. Since the parameter selected for the expansion is typically estimated to be small, the perturbative approach turns out to be adequate to our purpose. Using results on affine models, the extended CIR model is estimated via maximum likelihood on a time series of daily interest rate yields. Results show that the CIR model has to be rejected with respect to the proposed extension, and it is pointed out that the extended CIR model provides a more flexible characterization of the link between risk neutral and natural probability. Journal: Applied Mathematical Finance Pages: 143-153 Issue: 2 Volume: 13 Year: 2006 X-DOI: 10.1080/13504860500395943 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860500395943 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:2:p:143-153 Template-Type: ReDIF-Article 1.0 Author-Name: Yoshifumi Muroi Author-X-Name-First: Yoshifumi Author-X-Name-Last: Muroi Title: Pricing Lookback Options with Knock-out Boundaries Abstract: In the last decade, many kinds of exotic options have been traded and introduced in the financial market. This paper describes a new kind of exotic option, lookback options with knock-out boundaries. These options are knock-out options whose pay-offs depend on the extrema of a given securities price over a certain period of time. Closed form expressions for the price of seven kinds of lookback options with knock-out boundaries are obtained in this article. The numerical studies have also been presented. Journal: Applied Mathematical Finance Pages: 155-190 Issue: 2 Volume: 13 Year: 2006 Keywords: Exotic options, lookback options, knock-out boundaries, X-DOI: 10.1080/13504860600563028 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600563028 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:2:p:155-190 Template-Type: ReDIF-Article 1.0 Author-Name: C. Atkinson Author-X-Name-First: C. Author-X-Name-Last: Atkinson Author-Name: C. A. Alexandropoulos Author-X-Name-First: C. A. Author-X-Name-Last: Alexandropoulos Title: Pricing a European Basket Option in the Presence of Proportional Transaction Costs Abstract: A crucial assumption in the Black-Scholes theory of options pricing is the no transaction costs assumption. However, following such a strategy in the presence of transaction costs would lead to immediate ruin. This paper presents a stochastic control approach to the pricing and hedging of a European basket option, dependent on primitive assets whose prices are modelled as lognormal diffusions, in the presence of costs proportional to the size of the transaction. Under certain assumptions on the individual preferences, it is able to reduce the dimensionality of the resulting control problem. This facilitates considerably the study of the value function and the characterisation of the optimal trading policy. For solution of the problem a perturbation analysis scheme is utilized to derive a non-trivial, asymptotically optimal result. The findings reveal that this result can be expressed by means of a small correction to the corresponding solution of the frictionless Black-Scholes type problem, resembling a multi-dimensional 'bandwidth' around the vanilla case, which, moreover, is readily tractable. Journal: Applied Mathematical Finance Pages: 191-214 Issue: 3 Volume: 13 Year: 2006 Keywords: Option pricing, transaction costs, utility function, asymptotic expansion, Hamilton-Jacobi-Bellman equation, closed form solution, X-DOI: 10.1080/13504860600563184 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600563184 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:3:p:191-214 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Pierre Fouque Author-X-Name-First: Jean-Pierre Author-X-Name-Last: Fouque Author-Name: Ronnie Sircar Author-X-Name-First: Ronnie Author-X-Name-Last: Sircar Author-Name: Knut Sølna Author-X-Name-First: Knut Author-X-Name-Last: Sølna Title: Stochastic Volatility Effects on Defaultable Bonds Abstract: This paper studies the effect of introducing stochastic volatility in the first-passage structural approach to default risk. The impact of volatility time scales on the yield spread curve is analyzed. In particular it is shown that the presence of a short time scale in the volatility raises the yield spreads at short maturities. It is argued that combining first passage default modelling with multiscale stochastic volatility produces more realistic yield spreads. Moreover, this framework enables the use of perturbation techniques to derive explicit approximations which facilitate the complicated issue of calibration of parameters. Journal: Applied Mathematical Finance Pages: 215-244 Issue: 3 Volume: 13 Year: 2006 Keywords: First-passage structural approach, stochastic volatility, time scales, yield spreads, calibration, X-DOI: 10.1080/13504860600563127 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600563127 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:3:p:215-244 Template-Type: ReDIF-Article 1.0 Author-Name: Fima Klebaner Author-X-Name-First: Fima Author-X-Name-Last: Klebaner Author-Name: Truc Le Author-X-Name-First: Truc Author-X-Name-Last: Le Author-Name: Robert Liptser Author-X-Name-First: Robert Author-X-Name-Last: Liptser Title: On Estimation of Volatility Surface and Prediction of Future Spot Volatility Abstract: A stochastic process v(t) is considered as a model for asset's spot volatility. A new approach is introduced for predicting future spot volatility and future volatility surface using a finite set of observed option prices. When the volatility parameter σ2 in the Black-Scholes formula[image omitted]   is represented by the integrated volatility [image omitted]   , then the local volatility surface can be estimated. The main idea is to linearize the expressions for implied volatility by using a result on Normal correlation. This linearization is obtained by introducing various ad hoc approximations. Journal: Applied Mathematical Finance Pages: 245-263 Issue: 3 Volume: 13 Year: 2006 X-DOI: 10.1080/13504860600564661 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600564661 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:3:p:245-263 Template-Type: ReDIF-Article 1.0 Author-Name: M. H. Vellekoop Author-X-Name-First: M. H. Author-X-Name-Last: Vellekoop Author-Name: J. W. Nieuwenhuis Author-X-Name-First: J. W. Author-X-Name-Last: Nieuwenhuis Title: Efficient Pricing of Derivatives on Assets with Discrete Dividends Abstract: It is argued that due to inconsistencies in existing methods to approximate the prices of equity options on assets which pay out fixed cash dividends at future dates, a new approach to this problem may be useful. Logically consistent methods which are guaranteed to exclude arbitrage exist, but they are not very popular in practice due to their computational complexity. An algorithm is defined which is easy to understand, computationally efficient, and which guarantees to generate prices which exclude arbitrage possibilitites. It is shown that for the method to work a mild uniform convergence condition must be satisfied and this condition is indeed satisfied for standard European and American options. Numerical results testify to the accuracy and flexibility of the method. Journal: Applied Mathematical Finance Pages: 265-284 Issue: 3 Volume: 13 Year: 2006 Keywords: Equity option, pricing dividends, numerical methods, X-DOI: 10.1080/13504860600563077 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600563077 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:3:p:265-284 Template-Type: ReDIF-Article 1.0 Author-Name: Fernando Durrell Author-X-Name-First: Fernando Author-X-Name-Last: Durrell Title: Optimum Constrained Portfolio Rules in a Diffusion Market Abstract: A portfolio selection model is derived for diffusions where inequality constraints are imposed on portfolio security weights. Using the method of stochastic dynamic programming Hamilton-Jacobi-Bellman (HJB) equations are obtained for the problem of maximizing the expected utility of terminal wealth over a finite time horizon. Optimal portfolio weights are given in feedback form in terms of the solution of the HJB equations and its partial derivatives. An analysis of the no-constraining (NC) region of a portfolio is also conducted. Journal: Applied Mathematical Finance Pages: 285-307 Issue: 4 Volume: 13 Year: 2006 Keywords: Utility, stochastic dynamic programming, Hamilton-Jacobi-Bellman equation, constraints, X-DOI: 10.1080/13504860600840061 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600840061 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:285-307 Template-Type: ReDIF-Article 1.0 Author-Name: Massimo Morini Author-X-Name-First: Massimo Author-X-Name-Last: Morini Author-Name: Nick Webber Author-X-Name-First: Nick Author-X-Name-Last: Webber Title: An EZI Method to Reduce the Rank of a Correlation Matrix in Financial Modelling Abstract: Reducing the number of factors in a model by reducing the rank of a correlation matrix is a problem that often arises in finance, for instance in pricing interest rate derivatives with Libor market models. A simple iterative algorithm for correlation rank reduction is introduced, the eigenvalue zeroing by iteration, EZI, algorithm. Its convergence is investigated and extension presented with particular optimality properties. The performance of EZI is compared with those of other common methods. Different data sets are considered including empirical data from the interest rate market, different possible market cases and criteria, and a calibration case. The EZI algorithm is extremely fast even in computationally complex situations, and achieves a very high level of precision. From these results, the EZI algorithm for financial application has superior performance to the main methods in current use. Journal: Applied Mathematical Finance Pages: 309-331 Issue: 4 Volume: 13 Year: 2006 Keywords: Correlation matrix, rank reduction, market models, X-DOI: 10.1080/13504860600658976 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600658976 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:309-331 Template-Type: ReDIF-Article 1.0 Author-Name: Claudia Ribeiro Author-X-Name-First: Claudia Author-X-Name-Last: Ribeiro Author-Name: Nick Webber Author-X-Name-First: Nick Author-X-Name-Last: Webber Title: Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes Abstract: Levy processes can be used to model asset return's distributions. Monte Carlo methods must frequently be used to value path dependent options in these models, but Monte Carlo methods can be prone to considerable simulation bias when valuing options with continuous reset conditions. This paper shows how to correct for this bias for a range of options by generating a sample from the extremes distribution of the Levy process on subintervals. The method uses variance-gamma and normal inverse Gaussian processes. The method gives considerable reductions in bias, so that it becomes feasible to apply variance reduction methods. The method seems to be a very fruitful approach in a framework in which many options do not have analytical solutions. Journal: Applied Mathematical Finance Pages: 333-352 Issue: 4 Volume: 13 Year: 2006 Keywords: Bridge monte carlo methods, simulations bias, exotic options valuation, levy processes, X-DOI: 10.1080/13504860600658992 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600658992 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:333-352 Template-Type: ReDIF-Article 1.0 Author-Name: H. A. Windcliff Author-X-Name-First: H. A. Author-X-Name-Last: Windcliff Author-Name: P. A. Forsyth Author-X-Name-First: P. A. Author-X-Name-Last: Forsyth Author-Name: K. R. Vetzal Author-X-Name-First: K. R. Author-X-Name-Last: Vetzal Title: Numerical Methods and Volatility Models for Valuing Cliquet Options Abstract: Several numerical issues for valuing cliquet options using PDE methods are investigated. The use of a running sum of returns formulation is compared to an average return formulation. Methods for grid construction, interpolation of jump conditions, and application of boundary conditions are compared. The effect of various volatility modelling assumptions on the value of cliquet options is also studied. Numerical results are reported for jump diffusion models, calibrated volatility surface models, and uncertain volatility models. Journal: Applied Mathematical Finance Pages: 353-386 Issue: 4 Volume: 13 Year: 2006 Keywords: Cliquet options, jump diffusion, interpolation, boundary conditions, volatility models, X-DOI: 10.1080/13504860600839964 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600839964 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:13:y:2006:i:4:p:353-386 Template-Type: ReDIF-Article 1.0 Author-Name: James Primbs Author-X-Name-First: James Author-X-Name-Last: Primbs Author-Name: Muruhan Rathinam Author-X-Name-First: Muruhan Author-X-Name-Last: Rathinam Author-Name: Yuji Yamada Author-X-Name-First: Yuji Author-X-Name-Last: Yamada Title: Option Pricing with a Pentanomial Lattice Model that Incorporates Skewness and Kurtosis Abstract: This paper analyzes a pentanomial lattice model for option pricing that incorporates skewness and kurtosis of the underlying asset. The lattice is constructed using a moment matching procedure, and explicit positivity conditions for branch probabilities are provided in terms of skewness and kurtosis. We also explore the limiting distribution of this lattice, which is compound Poisson, and give a Fourier transform based formula that can be used to more efficiently price European call and put options. An example illustrates some of the features of this model in capturing volatility smiles and smirks. Journal: Applied Mathematical Finance Pages: 1-17 Issue: 1 Volume: 14 Year: 2007 Keywords: Lattice, volatility smile, option pricing, X-DOI: 10.1080/13504860600659172 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600659172 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:1-17 Template-Type: ReDIF-Article 1.0 Author-Name: Leonard Tchuindjo Author-X-Name-First: Leonard Author-X-Name-Last: Tchuindjo Title: Pricing of Multi-Defaultable Bonds with a Two-Correlated-Factor Hull-White Model Abstract: This research attempts to propose closed-form solutions for prices of credit-risky bonds, assuming a nonzero correlation between interest rates and credit spreads. The times of default of a credit-risky bond are modelled as the jump times of a Cox process, following the method of Lando, with an intensity that follows a Hull and White model, correlated with a similar model of the risk-free interest rate. Under the fractional recovery of market value assumption of Duffie and Singleton, the partial differential equation (PDE) for the price of the zero-coupon credit-risky bond is derived. Then this PDE is analytically solved, using the method of separation of variables, and easy-to-implement closed-form solutions are found. Finally, numerical examples are presented to show how these closed-form solutions can identify the magnitude and the direction of the credit-risky bond mispricing under different parameter assumptions. Journal: Applied Mathematical Finance Pages: 19-39 Issue: 1 Volume: 14 Year: 2007 Keywords: PDE, Cox process, credit spread, defaultable bond, Hull and White model, X-DOI: 10.1080/13504860600658943 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600658943 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:19-39 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Elliott Author-X-Name-First: Robert Author-X-Name-Last: Elliott Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Leunglung Chan Author-X-Name-First: Leunglung Author-X-Name-Last: Chan Title: Pricing Volatility Swaps Under Heston's Stochastic Volatility Model with Regime Switching Abstract: A model is developed for pricing volatility derivatives, such as variance swaps and volatility swaps under a continuous-time Markov-modulated version of the stochastic volatility (SV) model developed by Heston. In particular, it is supposed that the parameters of this version of Heston's SV model depend on the states of a continuous-time observable Markov chain process, which can be interpreted as the states of an observable macroeconomic factor. The market considered is incomplete in general, and hence, there is more than one equivalent martingale pricing measure. The regime switching Esscher transform used by Elliott et al. is adopted to determine a martingale pricing measure for the valuation of variance and volatility swaps in this incomplete market. Both probabilistic and partial differential equation (PDE) approaches are considered for the valuation of volatility derivatives. Journal: Applied Mathematical Finance Pages: 41-62 Issue: 1 Volume: 14 Year: 2007 Keywords: Regime switching Esscher transform, Markov-modulated Heston's SV model, observable Markov chain process, volatility swaps, variance swaps, regime switching OU-process, X-DOI: 10.1080/13504860600659222 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600659222 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:41-62 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Howison Author-X-Name-First: Sam Author-X-Name-Last: Howison Author-Name: Mario Steinberg Author-X-Name-First: Mario Author-X-Name-Last: Steinberg Title: A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 1: Barrier Options Abstract: This paper discusses the 'continuity correction' that should be applied to relate the prices of discretely sampled barrier options and their continuously-sampled equivalents. Using a matched asymptotic expansions approach it is shown that the correction of Broadie, Glasserman & Kou (Mathematical Finance 7, 325 (1997)) can be applied in a very wide variety of cases. The correction to higher order is calculated in terms of the expansion parameter (the scaled time between resets) and it is shown how to apply the correction in jump-diffusion and local volatility models. Journal: Applied Mathematical Finance Pages: 63-89 Issue: 1 Volume: 14 Year: 2007 X-DOI: 10.1080/13504860600858402 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600858402 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:63-89 Template-Type: ReDIF-Article 1.0 Author-Name: Sam Howison Author-X-Name-First: Sam Author-X-Name-Last: Howison Title: A Matched Asymptotic Expansions Approach to Continuity Corrections for Discretely Sampled Options. Part 2: Bermudan Options Abstract: The paper discusses the 'continuity correction' that should be applied to connect the prices of discretely sampled American put options (i.e. Bermudan options) and their continuously-sampled equivalents. Using a matched asymptotic expansions approach the correction is computed and related to that discussed by Broadie, Glasserman & Kou (1997) (Mathematical Finance, 7, p.325 for barrier options. In the Bermudan case, the continuity correction is an order of magnitude smaller than in the corresponding barrier problem. It is also shown that the optimal exercise boundary in the discrete case is slightly higher than in the continuously sampled case. Journal: Applied Mathematical Finance Pages: 91-104 Issue: 1 Volume: 14 Year: 2007 X-DOI: 10.1080/13504860600858410 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600858410 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:91-104 Template-Type: ReDIF-Article 1.0 Author-Name: Roger Lord Author-X-Name-First: Roger Author-X-Name-Last: Lord Author-Name: Antoon Pelsser Author-X-Name-First: Antoon Author-X-Name-Last: Pelsser Title: Level-Slope-Curvature - Fact or Artefact? Abstract: The first three factors resulting from a principal components analysis of term structure data are, in the literature, typically interpreted as driving the level, slope and curvature of the term structure. Using slight generalizations of theorems from total positivity, we present sufficient conditions under which level, slope and curvature are present. These conditions have the nice interpretation of restricting the level, slope and curvature of the correlation surface. It is proven that the Schoenmakers-Coffey correlation matrix also brings along such factors. Finally, we formulate and corroborate a conjecture that the order present in correlation matrices cause slope. Journal: Applied Mathematical Finance Pages: 105-130 Issue: 2 Volume: 14 Year: 2007 Keywords: Principal components analysis, correlation matrix, term structure, total positivity, oscillation matrix, Schoenmakers-Coffey matrix, X-DOI: 10.1080/13504860600661111 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600661111 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:105-130 Template-Type: ReDIF-Article 1.0 Author-Name: Ariel Almendral Author-X-Name-First: Ariel Author-X-Name-Last: Almendral Author-Name: Cornelis W. Oosterlee Author-X-Name-First: Cornelis W. Author-X-Name-Last: Oosterlee Title: On American Options Under the Variance Gamma Process Abstract: American options are considered in a market where the underlying asset follows a Variance Gamma process. A sufficient condition is given for the failure of the smooth fit principle for finite horizon call options. A second-order accurate finite-difference method is proposed to find the American option price and the exercise boundary. The problem is formulated as a Linear Complementarity Problem and solved numerically by a convenient splitting. Computations have been accelerated with the help of the Fast Fourier Transform. A stability analysis shows that the scheme is conditionally stable, with a mild stability condition of the form k = O(&7Clog(h)&7C-1). The theoretical results are verified numerically throughout a series of numerical experiments. Journal: Applied Mathematical Finance Pages: 131-152 Issue: 2 Volume: 14 Year: 2007 Keywords: Integro-differential equations, variance gamma, finite differences, FFT, X-DOI: 10.1080/13504860600724885 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600724885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:131-152 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Author-Name: Jan Kallsen Author-X-Name-First: Jan Author-X-Name-Last: Kallsen Author-Name: Thilo Meyer-Brandis Author-X-Name-First: Thilo Author-X-Name-Last: Meyer-Brandis Title: A Non-Gaussian Ornstein-Uhlenbeck Process for Electricity Spot Price Modeling and Derivatives Pricing Abstract: A mean-reverting model is proposed for the spot price dynamics of electricity which includes seasonality of the prices and spikes. The dynamics is a sum of non-Gaussian Ornstein-Uhlenbeck processes with jump processes giving the normal variations and spike behaviour of the prices. The amplitude and frequency of jumps may be seasonally dependent. The proposed dynamics ensures that spot prices are positive, and that the dynamics is simple enough to allow for analytical pricing of electricity forward and futures contracts. Electricity forward and futures contracts have the distinctive feature of delivery over a period rather than at a fixed point in time, which leads to quite complicated expressions when using the more traditional multiplicative models for spot price dynamics. In a simulation example it is demonstrated that the model seems to be sufficiently flexible to capture the observed dynamics of electricity spot prices. The pricing of European call and put options written on electricity forward contracts is also discussed. Journal: Applied Mathematical Finance Pages: 153-169 Issue: 2 Volume: 14 Year: 2007 Keywords: Electricity markets, spot price modelling, forward and futures pricing, additive processes, Ornstein-Uhlenbeck processes, X-DOI: 10.1080/13504860600725031 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600725031 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:153-169 Template-Type: ReDIF-Article 1.0 Author-Name: E. Eberlein Author-X-Name-First: E. Author-X-Name-Last: Eberlein Author-Name: J. Liinev Author-X-Name-First: J. Author-X-Name-Last: Liinev Title: The Levy Swap Market Model Abstract: Models driven by Levy processes are attractive since they allow for better statistical fitting than classical diffusion models. The dynamics of the forward swap rate process is derived in a semimartingale setting and a Levy swap market model is introduced. In order to guarantee positive rates, the swap rates are modelled as ordinary exponentials. The model starts with the most distant rate, which is driven by a non-homogeneous Levy process. Via backward induction the remaining swap rates are constructed such that they become martingales under the corresponding forward swap measures. Finally it is shown how swaptions can be priced using bilateral Laplace transforms. Journal: Applied Mathematical Finance Pages: 171-196 Issue: 2 Volume: 14 Year: 2007 Keywords: Swap rates, swap market model, swaption, forward swap measure, Levy process, interest rate model, X-DOI: 10.1080/13504860600724950 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600724950 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:2:p:171-196 Template-Type: ReDIF-Article 1.0 Author-Name: Mark S. Joshi Author-X-Name-First: Mark S. Author-X-Name-Last: Joshi Title: A Simple Derivation of and Improvements to Jamshidian's and Rogers' Upper Bound Methods for Bermudan Options Abstract: The additive method for upper bounds for Bermudan options is rephrased in terms of buyer's and seller's prices. It is shown how to deduce Jamshidian's upper bound result in a simple fashion from the additive method, including the case of possibly zero final pay-off. Both methods are improved by ruling out exercise at sub-optimal points. It is also shown that it is possible to use sub-Monte Carlo simulations to estimate the value of the hedging portfolio at intermediate points in the Jamshidian method without jeopardizing its status as upper bound. Journal: Applied Mathematical Finance Pages: 197-205 Issue: 3 Volume: 14 Year: 2007 Keywords: Monte Carlo, Bermudan options, early exercise, upper bounds, X-DOI: 10.1080/13504860600858071 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600858071 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:3:p:197-205 Template-Type: ReDIF-Article 1.0 Author-Name: Fabricio Tourrucoo Author-X-Name-First: Fabricio Author-X-Name-Last: Tourrucoo Author-Name: Patrick S. Hagan Author-X-Name-First: Patrick S. Author-X-Name-Last: Hagan Author-Name: Gilberto F. Schleiniger Author-X-Name-First: Gilberto F. Author-X-Name-Last: Schleiniger Title: Approximate Formulas for Zero-coupon Bonds Abstract: Using perturbation methods, approximate formulas are obtained for zero-coupon bonds under the generalized Black-Karasinski model. The formulas perform well regarding accuracy and calibration to available data. For a special case, which corresponds to the Hull-White model, the approximation actually yields an exact solution. Numerical simulations are presented that partially validate the asymptotic approximation. A calibration strategy is investigated in order to fit the model to given data on discount rates. Journal: Applied Mathematical Finance Pages: 207-226 Issue: 3 Volume: 14 Year: 2007 Keywords: Perturbation methods, pricing fixed-income instruments, generalized Black-Karasinski model, approximate and exact solutions, calibration, X-DOI: 10.1080/13504860600858204 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600858204 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:3:p:207-226 Template-Type: ReDIF-Article 1.0 Author-Name: Alessio Sancetta Author-X-Name-First: Alessio Author-X-Name-Last: Sancetta Author-Name: Steve E. Satchell Author-X-Name-First: Steve E. Author-X-Name-Last: Satchell Title: Changing Correlation and Equity Portfolio Diversification Failure for Linear Factor Models during Market Declines* Abstract: The paper considers a linear factor model (LFM) to study the behaviour of the correlation coefficient between various stock returns during a downturn. Changing correlation is related to the tail distribution of the driving factors, which is the market for Sharpe's one-factor model. General classes of distribution functions are considered and asymptotic conditions found on the tails of the distribution, which determine whether diversification will succeed or fail during a market decline. Journal: Applied Mathematical Finance Pages: 227-242 Issue: 3 Volume: 14 Year: 2007 Keywords: Asymptotic Expansion, Factor Model, Portfolio Diversification, Truncated Variance, X-DOI: 10.1080/13504860600858279 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600858279 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:3:p:227-242 Template-Type: ReDIF-Article 1.0 Author-Name: Fredrik Armerin Author-X-Name-First: Fredrik Author-X-Name-Last: Armerin Author-Name: Bjarne Astrup Jensen Author-X-Name-First: Bjarne Astrup Author-X-Name-Last: Jensen Author-Name: Tomas Bjork Author-X-Name-First: Tomas Author-X-Name-Last: Bjork Title: Term Structure Models with Parallel and Proportional Shifts Abstract: The paper investigates the possibility of an arbitrage-free model for the term structure of interest rates where the yield curve only changes through a parallel shift. HJM type forward rate models driven by a multidimensional Wiener process and by a general marked point process are considered. Within this general framework it is shown that there does indeed exist a large variety of nontrivial parallel shift term structure models, and we also describe these in detail. It is also shown that there exists no nontrivial flat term structure model. The same analysis is repeated for a similar case, in which the yield curve only changes through proportional shifts. Journal: Applied Mathematical Finance Pages: 243-260 Issue: 3 Volume: 14 Year: 2007 Keywords: bond market, term structure of interest rates, flat term structures, X-DOI: 10.1080/13504860600858030 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600858030 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:3:p:243-260 Template-Type: ReDIF-Article 1.0 Author-Name: Joanna Goard Author-X-Name-First: Joanna Author-X-Name-Last: Goard Title: Using Utility Functions to Model Risky Bonds Abstract: This paper prices defaultable bonds by incorporating inherent risks with the use of utility functions. By allowing risk preferences into the valuation of bonds, nonlinearity is introduced in their pricing. The utility-function approach affords the advantage of yielding exact solutions to the risky bond pricing equation when familiar stochastic models are used for interest rates. This can be achieved even when the default probability parameter is itself a stochastic variable. Valuations are found for the power-law and log utility functions under the interest-rate dynamics of the extended Vasicek and CIR models. Journal: Applied Mathematical Finance Pages: 261-289 Issue: 3 Volume: 14 Year: 2007 Keywords: utility functions, risky bonds, defaultable bonds, X-DOI: 10.1080/13504860600951652 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600951652 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:3:p:261-289 Template-Type: ReDIF-Article 1.0 Author-Name: Oh Kang Kwon Author-X-Name-First: Oh Kang Author-X-Name-Last: Kwon Title: Mean Reversion Level Extensions of Time-Homogeneous Affine Term Structure Models Abstract: It is well-known that time-homogeneous affine term structure models are incompatible with most observed initial forward rate curves. For the Vasicek (1977) and Cox et al. (1985) models, time-inhomogeneous extensions capable of fitting any given initial forward rate curve were introduced in Hull and White (1990), and similar extensions, for short rate models in general, were introduced in Bjork and Hyll (2000), Brigo and Mercurio (2001), and Kwon (2004). In this paper, we introduce a general and systematic method for obtaining time-inhomogeneous extensions of affine term structure models that are compatible with any observed initial forward rate curve. These extensions are minimal in the sense that the system of Riccati equations determining the bond prices remain essentially unchanged under the extension. Moreover, the extensions considered in Bjork and Hyll (2000), Brigo and Mercurio (2001), and Kwon (2004), for time-homogeneous affine term structure models, are all special cases of the extensions introduced in this paper. Journal: Applied Mathematical Finance Pages: 291-302 Issue: 4 Volume: 14 Year: 2007 Keywords: Affine term structure model, mean reversion level, initial forward rate curve, time-inhomogeous extension, X-DOI: 10.1080/13504860600951686 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860600951686 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:291-302 Template-Type: ReDIF-Article 1.0 Author-Name: M. R. Grasselli Author-X-Name-First: M. R. Author-X-Name-Last: Grasselli Author-Name: T. R. Hurd Author-X-Name-First: T. R. Author-X-Name-Last: Hurd Title: Indifference Pricing and Hedging for Volatility Derivatives Abstract: Utility based indifference pricing and hedging are now considered to be an economically natural method for valuing contingent claims in incomplete markets. However, acceptance of these concepts by the wide financial community has been hampered by the computational and conceptual difficulty of the approach. This paper focuses on the problem of computing indifference prices for derivative securities in a class of incomplete stochastic volatility models general enough to include important examples. A rigorous development is presented based on identifying the natural martingales in the model, leading to a nonlinear Feynman-Kac representation for the indifference price of contingent claims on volatility. To illustrate the power of this representation, closed form solutions are given for the indifference price of a variance swap in the standard Heston model and in a new “reciprocal Heston” model. These are the first known explicit formulas for the indifference price for a class of derivatives that is important to the finance industry. Journal: Applied Mathematical Finance Pages: 303-317 Issue: 4 Volume: 14 Year: 2007 Keywords: Volatility risk, exponential utility, Heston model, variance swap, incomplete markets, certainty equivalent, volatility derivative, X-DOI: 10.1080/13527260600963851 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13527260600963851 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:303-317 Template-Type: ReDIF-Article 1.0 Author-Name: Nikolai Dokuchaev Author-X-Name-First: Nikolai Author-X-Name-Last: Dokuchaev Title: Mean-Reverting Market Model: Speculative Opportunities and Non-Arbitrage Abstract: The paper studies arbitrage opportunities and possible speculative opportunities for diffusion mean-reverting market models. It is shown that the Novikov condition is satisfied for any time interval and for any set of parameters. It is non-trivial because the appreciation rate has Gaussian distribution converging to a stationary limit. It follows that the mean-reverting model is arbitrage-free for any finite time interval. Further, it is shown that this model still allows some speculative opportunities: a gain for a wide enough set of expected utilities can be achieved for a strategy that does not require any hypothesis on market parameters and does not use estimation of these parameters. Journal: Applied Mathematical Finance Pages: 319-337 Issue: 4 Volume: 14 Year: 2007 Keywords: Diffusion market, mean-reverting model, arbitrage, technical analysis, self-financing strategies, universal portfolio, X-DOI: 10.1080/13504860701255078 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701255078 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:319-337 Template-Type: ReDIF-Article 1.0 Author-Name: Jia-Hau Guo Author-X-Name-First: Jia-Hau Author-X-Name-Last: Guo Author-Name: Mao-Wei Hung Author-X-Name-First: Mao-Wei Author-X-Name-Last: Hung Title: A Note on the Discontinuity Problem in Heston's Stochastic Volatility Model Abstract: Although quasi-analytic formulas can be derived for European-style financial claims in Heston's stochastic volatility model, the inverse Fourier integration involved makes the calculation somewhat complicated. This challenge has puzzled practitioners for many years because most implementations of Heston's formula are not robust, even for customarily-used Heston parameters, as time to maturity is increased. In this article, a simplified approach is proposed to solve the numerical instability problem inherent to the fundamental solution of the Heston model. Specifically, the solution does not require any additional function or a particular mechanism for most software packages or programming library routines to correctly evaluate Heston's analytics. Journal: Applied Mathematical Finance Pages: 339-345 Issue: 4 Volume: 14 Year: 2007 Keywords: Stochastic volatility model, Heston, discountinuity, options, X-DOI: 10.1080/13504860601170534 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860601170534 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:339-345 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Author-Name: Martin Groth Author-X-Name-First: Martin Author-X-Name-Last: Groth Author-Name: Rodwell Kufakunesu Author-X-Name-First: Rodwell Author-X-Name-Last: Kufakunesu Title: Valuing Volatility and Variance Swaps for a Non-Gaussian Ornstein-Uhlenbeck Stochastic Volatility Model Abstract: Following the increasing awareness of the risk from volatility fluctuations, the market for hedging contracts written on realized volatility has surged. Companies looking for means to secure against unexpected accumulation of market activity can find over-the-counter products written on volatility indices. Since the Black and Scholes model require a constant volatility the need to consider other models is obvious. Swaps written on powers of realized volatility in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard are investigated. A key formula is derived for the realized variance able to represent the swap price dynamics in terms of Laplace transforms, which makes fast numerical inversion methods viable. An example using the fast Fourier transform is shown and compared with the approximation proposed by Brockhaus and Long. Journal: Applied Mathematical Finance Pages: 347-363 Issue: 4 Volume: 14 Year: 2007 Keywords: Risk, hedging contracts, realized volatility, stochastic volatility, Levy processes, Laplace transforms, X-DOI: 10.1080/13504860601170609 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860601170609 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:4:p:347-363 Template-Type: ReDIF-Article 1.0 Author-Name: Carl Chiarella Author-X-Name-First: Carl Author-X-Name-Last: Chiarella Author-Name: Christina Nikitopoulos Sklibosios Author-X-Name-First: Christina Nikitopoulos Author-X-Name-Last: Sklibosios Author-Name: Erik Schlogl Author-X-Name-First: Erik Author-X-Name-Last: Schlogl Title: A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps Abstract: This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process. The pricing framework adapted was developed by Chiarella and Nikitopoulos to provide an extension of the Heath, Jarrow and Morton model to jump-diffusions and achieves Markovian structures under certain volatility specifications. Fourier Transform solutions for the price of a bond option under deterministic volatility specifications are derived and a control variate numerical method is developed under a more general state dependent volatility structure, a case in which closed form solutions are generally not possible. In doing so, a novel perspective is provided on control variate methods by going outside a given complex model to a simpler more tractable setting to provide the control variates. Journal: Applied Mathematical Finance Pages: 365-399 Issue: 5 Volume: 14 Year: 2007 Keywords: HJM model, jump process, bond option prices, control variate, Monte Carlo simulations, X-DOI: 10.1080/13504860701255359 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701255359 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:5:p:365-399 Template-Type: ReDIF-Article 1.0 Author-Name: S. V. Stoyanov Author-X-Name-First: S. V. Author-X-Name-Last: Stoyanov Author-Name: S. T. Rachev Author-X-Name-First: S. T. Author-X-Name-Last: Rachev Author-Name: F. J. Fabozzi Author-X-Name-First: F. J. Author-X-Name-Last: Fabozzi Title: Optimal Financial Portfolios Abstract: The classes of reward-risk optimization problems that arise from different choices of reward and risk measures are considered. In certain examples the generic problem reduces to linear or quadratic programming problems. An algorithm based on a sequence of convex feasibility problems is given for the general quasi-concave ratio problem. Reward-risk ratios that are appropriate in particular for non-normal assets return distributions and are not quasi-concave are also considered. Journal: Applied Mathematical Finance Pages: 401-436 Issue: 5 Volume: 14 Year: 2007 Keywords: Reward-risk ratio, optimal portfolio, risk measure, efficent frontier, X-DOI: 10.1080/13504860701255292 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701255292 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:5:p:401-436 Template-Type: ReDIF-Article 1.0 Author-Name: Birgit Rudloff Author-X-Name-First: Birgit Author-X-Name-Last: Rudloff Title: Convex Hedging in Incomplete Markets Abstract: In incomplete financial markets not every contingent claim can be replicated by a self-financing strategy. The risk of the resulting shortfall can be measured by convex risk measures, recently introduced by Follmer and Schied (2002). The dynamic optimization problem of finding a self-financing strategy that minimizes the convex risk of the shortfall can be split into a static optimization problem and a representation problem. It follows that the optimal strategy consists in superhedging the modified claim [image omitted]   , where H is the payoff of the claim and [image omitted]   is a solution of the static optimization problem, an optimal randomized test. In this paper, necessary and sufficient optimality conditions are deduced for the static problem using convex duality methods. The solution of the static optimization problem turns out to be a randomized test with a typical 0-1-structure. Journal: Applied Mathematical Finance Pages: 437-452 Issue: 5 Volume: 14 Year: 2007 Keywords: hedging, shortfall risk, convex risk measures, convex duality, generalized Neyman-Pearson lemma, X-DOI: 10.1080/13504860701352206 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701352206 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:5:p:437-452 Template-Type: ReDIF-Article 1.0 Author-Name: Andrea Gamba Author-X-Name-First: Andrea Author-X-Name-Last: Gamba Author-Name: Lenos Trigeorgis Author-X-Name-First: Lenos Author-X-Name-Last: Trigeorgis Title: An Improved Binomial Lattice Method for Multi-Dimensional Options Abstract: A binomial lattice approach is proposed for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two simple ideas: a log-transformation of the underlying processes, which is step by step consistent with the continuous-time diffusions, and a change of basis of the asset span, to transform asset prices into uncorrelated processes. An additional transformation is applied to approximate driftless dynamics. Even if these features are simple and straightforward to implement, it is shown that they significantly improve the efficiency of the multi-dimensional binomial algorithm. A thorough test of efficiency is provided compared with most popular binomial and trinomial lattice approaches for multi-dimensional diffusions. Although the order of convergence is the same for all lattice approaches, the proposed method shows improved efficiency. Journal: Applied Mathematical Finance Pages: 453-475 Issue: 5 Volume: 14 Year: 2007 Keywords: Option pricing, binomial lattice, multi-dimensional diffusion, JEL classification: G13, X-DOI: 10.1080/13504860701532237 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701532237 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:14:y:2007:i:5:p:453-475 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Gerstner Author-X-Name-First: Thomas Author-X-Name-Last: Gerstner Author-Name: Markus Holtz Author-X-Name-First: Markus Author-X-Name-Last: Holtz Title: Valuation of Performance-Dependent Options Abstract: Performance-dependent options are financial derivatives whose payoff depends on the performance of one asset in comparison to a set of benchmark assets. This paper presents a novel approach to the valuation of general performance-dependent options. To this end, a multidimensional Black-Scholes model is used to describe the temporal development of the asset prices. The martingale approach then yields the fair price of such options as a multidimensional integral whose dimension is the number of stochastic processes used in the model. The integrand is typically discontinuous, which makes accurate solutions difficult to achieve by numerical approaches, though. Using tools from computational geometry, a pricing formula is derived which only involves the evaluation of several smooth multivariate normal distributions. This way, performance-dependent options can efficiently be priced even for high-dimensional problems as is shown by numerical results. Journal: Applied Mathematical Finance Pages: 1-20 Issue: 1 Volume: 15 Year: 2008 Keywords: Option pricing, multivariate integration, hyperplane arrangements, X-DOI: 10.1080/13504860601170492 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860601170492 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:1:p:1-20 Template-Type: ReDIF-Article 1.0 Author-Name: Suhas Nayak Author-X-Name-First: Suhas Author-X-Name-Last: Nayak Author-Name: George Papanicolaou Author-X-Name-First: George Author-X-Name-Last: Papanicolaou Title: Market Influence of Portfolio Optimizers Abstract: The paper reports on a study of the feedback effects induced by portfolio optimizers on the underlying asset prices. Through their interaction with reference traders, who trade based on some aggregate incomes process, they are assumed to move asset prices away from the standard log-normal model. With market clearing as the main constraint, the approximate dynamics of the asset price are solved analytically assuming that the wealth of the portfolio optimizers is small relative to the total market capitalization of the stock. The influence of portfolio optimizers when their wealth is not so small is also calculated numerically. There is good agreement between the numerical and analytical results when the wealth of the optimizers is small. It is found that portfolio optimizers influence the price of the risky asset so as to decrease its volatility. The optimal allocation to the risky asset also changes as a result of the portfolio optimizers' actions. In general, it is advantageous to hold more of the risky asset, relative to the log normal Merton model. Journal: Applied Mathematical Finance Pages: 21-40 Issue: 1 Volume: 15 Year: 2008 Keywords: Hamilton-Jacobi-Bellman equation, feedback, portfolio optimization, X-DOI: 10.1080/13504860701269285 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701269285 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:1:p:21-40 Template-Type: ReDIF-Article 1.0 Author-Name: N. K. Nomikos Author-X-Name-First: N. K. Author-X-Name-Last: Nomikos Author-Name: O. Soldatos Author-X-Name-First: O. Author-X-Name-Last: Soldatos Title: Using Affine Jump Diffusion Models for Modelling and Pricing Electricity Derivatives Abstract: A seasonal affine jump diffusion spike model with regime switching in the long-run equilibrium level is applied to model spot and forward prices in the Scandinavian power market. The spike part of the model incorporates different coefficients of mean reversion in the spike and normal variables and thus improves the spot-forward relationship, particularly at time periods when spikes occur. The regime switching part of the model contains two separate regimes to distinguish between periods of high and low water levels in the reservoirs, reflecting the availability of hydropower in the market. The performance of the models is compared with that of other models proposed in the literature in terms of fitting the observed term structure, as well as by generating simulated price paths that have the same statistical properties as the actual prices observed in the market. In particular, the model performs well in terms of capturing the spikes and explaining their fast mean reversion as well as in terms of reflecting the seasonal volatility observed in the market. These issues are very important for the pricing and hedging of derivative instruments. Journal: Applied Mathematical Finance Pages: 41-71 Issue: 1 Volume: 15 Year: 2008 Keywords: Regime-switching spike model, affine jump diffusion models, electricity derivatives, seasonal risk premium, JEL Classification: G13, G12 and G33, X-DOI: 10.1080/13504860701427362 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701427362 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:1:p:41-71 Template-Type: ReDIF-Article 1.0 Author-Name: E. Papageorgiou Author-X-Name-First: E. Author-X-Name-Last: Papageorgiou Author-Name: R. Sircar Author-X-Name-First: R. Author-X-Name-Last: Sircar Title: Multiscale Intensity Models for Single Name Credit Derivatives Abstract: We study the pricing of defaultable derivatives, such as bonds, bond options, and credit default swaps in the reduced form framework of intensity-based models. We use regular and singular perturbation expansions on the intensity of default from which we derive approximations for the pricing functions of these derivatives. In particular, we assume an Ornstein-Uhlenbeck process for the interest rate, and a two-factor diffusion model for the intensity of default. The approximation allows for computational efficiency in calibrating the model. Finally, empirical evidence on the existence of multiple scales is presented by the calibration of the model on corporate yield curves. Journal: Applied Mathematical Finance Pages: 73-105 Issue: 1 Volume: 15 Year: 2008 Keywords: Defaultable bond, credit default swap, defaultable bond option, asymptotic approximation, time scales, JEL classification: G12, G13, X-DOI: 10.1080/13504860701352222 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701352222 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:1:p:73-105 Template-Type: ReDIF-Article 1.0 Author-Name: Syoiti Ninomiya Author-X-Name-First: Syoiti Author-X-Name-Last: Ninomiya Author-Name: Nicolas Victoir Author-X-Name-First: Nicolas Author-X-Name-Last: Victoir Title: Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing Abstract: A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of pricing Asian options under the Heston stochastic volatility model. 2000 Mathematics Subject Classification, 65C30, 65C05. Journal: Applied Mathematical Finance Pages: 107-121 Issue: 2 Volume: 15 Year: 2008 Keywords: Heston model, numerical methods for stochastic differential equations, mathematical finance, quasi-Monte Carlo method, X-DOI: 10.1080/13504860701413958 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701413958 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:107-121 Template-Type: ReDIF-Article 1.0 Author-Name: H. Albrecher Author-X-Name-First: H. Author-X-Name-Last: Albrecher Author-Name: P. A. Mayer Author-X-Name-First: P. A. Author-X-Name-Last: Mayer Author-Name: W. Schoutens Author-X-Name-First: W. Author-X-Name-Last: Schoutens Title: General Lower Bounds for Arithmetic Asian Option Prices Abstract: This paper provides model-independent lower bounds for prices of arithmetic Asian options expressed through prices of European call options on the same underlying that are assumed to be observable in the market, and the corresponding subreplicating strategy is identified. The first bound relies on the no-arbitrage assumption only and turns out to perform satisfactorily in various situations. It is shown how the bound can be tightened under mild additional assumptions on the underlying market model. This considerably generalizes lower bounds in the literature, which are only available in the Black-Scholes world. Furthermore, it is illustrated how to adapt the procedure to the case where only a finite number of strikes is available in the market. As a by-product, the finite strike upper bound on the Asian call price of Hobson et al. (2005a), who considered basket options, is rederived. Numerical illustrations of the bounds are given together with comparisons to bounds resulting from model specifications. Journal: Applied Mathematical Finance Pages: 123-149 Issue: 2 Volume: 15 Year: 2008 Keywords: Asian options, model-independent bounds, no-arbitrage, static hedging, X-DOI: 10.1080/13527260701356633 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13527260701356633 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:123-149 Template-Type: ReDIF-Article 1.0 Author-Name: Ionuţ Florescu Author-X-Name-First: Ionuţ Author-X-Name-Last: Florescu Author-Name: Frederi Viens Author-X-Name-First: Frederi Author-X-Name-Last: Viens Title: Stochastic Volatility: Option Pricing using a Multinomial Recombining Tree Abstract: The problem of option pricing is treated using the Stochastic Volatility (SV) model: the volatility of the underlying asset is a function of an exogenous stochastic process, typically assumed to be mean-reverting. Assuming that only discrete past stock information is available, an interacting particle stochastic filtering algorithm due to Del Moral et al. (Del Moral et al., 2001) is adapted to estimate the SV, and a quadrinomial tree is constructed which samples volatilities from the SV filter's empirical measure approximation at time 0. Proofs of convergence of the tree to continuous-time SV models are provided. Classical arbitrage-free option pricing is performed on the tree, and provides answers that are close to market prices of options on the SP500 or on blue-chip stocks. Results obtained here are compared with those from non-random volatility models, and from models which continue to estimate volatility after time 0. It is shown precisely how to calibrate the incomplete market, choosing a specific martingale measure, by using a benchmark option. Journal: Applied Mathematical Finance Pages: 151-181 Issue: 2 Volume: 15 Year: 2008 Keywords: Incomplete markets, Monte Carlo method, options market, option pricing, particle method, random tree, stochastic filtering, stochastic volatility, X-DOI: 10.1080/13504860701596745 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701596745 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:151-181 Template-Type: ReDIF-Article 1.0 Author-Name: Thorsten Schmidt Author-X-Name-First: Thorsten Author-X-Name-Last: Schmidt Author-Name: Alexander Novikov Author-X-Name-First: Alexander Author-X-Name-Last: Novikov Title: A Structural Model with Unobserved Default Boundary Abstract: A firm-value model similar to the one proposed by Black and Cox (1976) is considered. Instead of assuming a constant and known default boundary, the default boundary is an unobserved stochastic process. This process has a Brownian component, reflecting the influence of uncertain effects on the precise timing of the default, and a jump component, which relates to abrupt changes in the policy of the company, exogenous events or changes in the debt structure. Interestingly, this setup admits a default intensity, so the reduced form methodology can be applied. Journal: Applied Mathematical Finance Pages: 183-203 Issue: 2 Volume: 15 Year: 2008 Keywords: Structural model, equity default swaps, default boundary, jump-diffusion, X-DOI: 10.1080/13504860701718281 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701718281 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:183-203 Template-Type: ReDIF-Article 1.0 Author-Name: E. Bayraktar Author-X-Name-First: E. Author-X-Name-Last: Bayraktar Title: Pricing Options on Defaultable Stocks Abstract: † Stock option price approximations are developed for a model which takes both the risk of default and the stochastic volatility into account. The intensity of defaults is assumed to be influenced by the volatility. It is shown that it might be possible to infer the risk neutral default intensity from the stock option prices. The proposed option price approximation has a rich implied volatility surface structure and fits the data implied volatility well. A calibration exercise shows that an effective hazard rate from bonds issued by a company can be used to explain the impliedvolatility skew of the option prices issued by the same company. It is also observed that the implied yield spread obtained from calibrating all the model parameters to the option prices matches the observed yield spread. Journal: Applied Mathematical Finance Pages: 277-304 Issue: 3 Volume: 15 Year: 2008 Keywords: Option pricing, multiscale perturbation methods, defaultable stocks, stochastic intensity of default, implied volatility skew, X-DOI: 10.1080/13504860701798283 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701798283 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:3:p:277-304 Template-Type: ReDIF-Article 1.0 Author-Name: S. Antes Author-X-Name-First: S. Author-X-Name-Last: Antes Author-Name: M. Ilg Author-X-Name-First: M. Author-X-Name-Last: Ilg Author-Name: B. Schmid Author-X-Name-First: B. Author-X-Name-Last: Schmid Author-Name: R. Zagst Author-X-Name-First: R. Author-X-Name-Last: Zagst Title: Empirical Evaluation of Hybrid Defaultable Bond Pricing Models Abstract: A four-factor model (the extended model of Schmid and Zagst) is presented for pricing credit risk related instruments such as defaultable bonds or credit derivatives. It is an advancement of an earlier three-factor model. In addition to a firm-specific credit risk factor, a new systematic risk factor in the form of GDP growth rate is included. This new model is set in the context of other hybrid defaultable bond pricing models and empirically compared to specific representatives. We find that a model based only on firm-specific variables is unable to capture changes in credit spreads completely. However, it is shown that in this model, market variables such as GDP growth rates, non-defaultable interest rates and firm-specific variables together significantly influence credit spread levels and changes. Journal: Applied Mathematical Finance Pages: 219-249 Issue: 3 Volume: 15 Year: 2008 X-DOI: 10.1080/13504860701718430 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701718430 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:3:p:219-249 Template-Type: ReDIF-Article 1.0 Author-Name: B. Peeters Author-X-Name-First: B. Author-X-Name-Last: Peeters Author-Name: C. L. Dert Author-X-Name-First: C. L. Author-X-Name-Last: Dert Author-Name: A. Lucas Author-X-Name-First: A. Author-X-Name-Last: Lucas Title: Hedging Large Portfolios of Options in Discrete Time Abstract: The problem studied is that of hedging a portfolio of options in discrete time where underlying security prices are driven by a combination of idiosyncratic and systematic risk factors. It is shown that despite the market incompleteness introduced by the discrete time assumption, large portfolios of options have a unique price and can be hedged without risk. The nature of the hedge portfolio in the limit of large portfolio size is substantially different from its continuous time counterpart. Instead of linearly hedging the total risk of each option separately, the correct portfolio hedge in discrete time eliminates linear as well as second and higher order exposures to the systematic risk factors only. The idiosyncratic risks need not be hedged, but disappear through diversification. Hedging portfolios of options in discrete time thus entails a trade-off between dynamic and cross-sectional hedging errors. Some computations are provided on the outcome of this trade-off in a discrete-time Black-Scholes world. Journal: Applied Mathematical Finance Pages: 251-275 Issue: 3 Volume: 15 Year: 2008 Keywords: Option hedging, discrete time, preference free valuation, hedging errors, cross-sectional hedging, static hedging, JEL Codes: G13, G12, X-DOI: 10.1080/13504860701718471 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701718471 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:3:p:251-275 Template-Type: ReDIF-Article 1.0 Author-Name: Mahmoud Zarepour Author-X-Name-First: Mahmoud Author-X-Name-Last: Zarepour Author-Name: Thierry Bedard Author-X-Name-First: Thierry Author-X-Name-Last: Bedard Author-Name: Andre Dabrowski Author-X-Name-First: Andre Author-X-Name-Last: Dabrowski Title: Return and Value at Risk using the Dirichlet Process Abstract: There exists a wide variety of models for return, and the chosen model determines the tool required to calculate the value at risk (VaR). This paper introduces an alternative methodology to model-based simulation by using a Monte Carlo simulation of the Dirichlet process. The model is constructed in a Bayesian framework, using properties initially described by Ferguson. A notable advantage of this model is that, on average, the random draws are sampled from a mixed distribution that consists of a prior guess by an expert and the empirical process based on a random sample of historical asset returns. The method is relatively automatic and similar to machine learning tools, e.g. the estimate is updated as new data arrive. Journal: Applied Mathematical Finance Pages: 205-218 Issue: 3 Volume: 15 Year: 2008 Keywords: Dirichlet process, quantiles, Bayes estimates, value at risk, X-DOI: 10.1080/13504860701718448 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701718448 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:3:p:205-218 Template-Type: ReDIF-Article 1.0 Author-Name: Grzegorz Hałaj Author-X-Name-First: Grzegorz Author-X-Name-Last: Hałaj Title: Risk-based Decisions on the Asset Structure of a Bank under Partial Economic Information Abstract: We present a model of a bank's dynamic asset management problem in the case of partially observed future economic conditions and with regulatory requirements governing the level of risk taken. The result is an optimal control problem with a random terminal condition arising from the partial observation of a parameter of a maximized functional. The Stochastic Maximum Principle reduces the problem to finding a solution to a Forward Backward Stochastic Differential Equation (FBSDE). As optimization usually implies the dependence of the forward equation on solutions of the backward equation we allow the drift and diffusion of the forward part to be functions of the solution of the backward equation. The necessary conditions for the existence of solutions of FBSDE in such a form are derived. A numerical scheme is then implemented to solve a particular case. Journal: Applied Mathematical Finance Pages: 305-329 Issue: 4 Volume: 15 Year: 2008 Keywords: Portfolio optimization, bank assets, partial observation, stochastic maximum principle, FBSDEs, X-DOI: 10.1080/13504860701852486 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701852486 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:305-329 Template-Type: ReDIF-Article 1.0 Author-Name: Mikael Elhouar Author-X-Name-First: Mikael Author-X-Name-Last: Elhouar Title: Finite-dimensional Realizations of Regime-switching HJM Models Abstract: This paper studies Heath-Jarrow-Morton-type models with regime-switching stochastic volatility. In this setting the forward rate volatility is allowed to depend on the current forward rate curve as well as on a continuous time Markov chain y with finitely many states. Employing the framework developed by Bjork and Svensson we find necessary and sufficient conditions on the volatility guaranteeing the representation of the forward rate process by a finite-dimensional Markovian state space model. These conditions allow us to investigate regime-switching generalizations of some well-known models such as those by Ho-Lee, Hull-White, and Cox-Ingersoll-Ross. Journal: Applied Mathematical Finance Pages: 331-354 Issue: 4 Volume: 15 Year: 2008 Keywords: HJM models, forward rates, stochastic volatility, state space models, Markov chains in continuous time, X-DOI: 10.1080/13504860801987133 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860801987133 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:331-354 Template-Type: ReDIF-Article 1.0 Author-Name: A. Zapranis Author-X-Name-First: A. Author-X-Name-Last: Zapranis Author-Name: A. Alexandridis Author-X-Name-First: A. Author-X-Name-Last: Alexandridis Title: Modelling the Temperature Time-dependent Speed of Mean Reversion in the Context of Weather Derivatives Pricing Abstract: In this paper, in the context of an Ornstein-Uhlenbeck temperature process, we use neural networks to examine the time dependence of the speed of the mean reversion parameter α of the process. We estimate non-parametrically with a neural network a model of the temperature process and then compute the derivative of the network output w.r.t. the network input, in order to obtain a series of daily values for α. To our knowledge, this is the first time that this has been done, and it gives us a much better insight into the temperature dynamics and temperature derivative pricing. Our results indicate strong time dependence in the daily values of α, and no seasonal patterns. This is important, since in all relevant studies performed thus far, α was assumed to be constant. Furthermore, the residuals of the neural network provide a better fit to the normal distribution when compared with the residuals of the classic linear models used in the context of temperature modelling (where α is constant). It follows that by setting the mean reversion parameter to be a function of time we improve the accuracy of the pricing of the temperature derivatives. Finally, we provide the pricing equations for temperature futures, when α is time dependent. Journal: Applied Mathematical Finance Pages: 355-386 Issue: 4 Volume: 15 Year: 2008 Keywords: Neural networks, weather derivatives pricing, X-DOI: 10.1080/13504860802006065 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802006065 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:355-386 Template-Type: ReDIF-Article 1.0 Author-Name: Hans-Peter Bermin Author-X-Name-First: Hans-Peter Author-X-Name-Last: Bermin Author-Name: Peter Buchen Author-X-Name-First: Peter Author-X-Name-Last: Buchen Author-Name: Otto Konstandatos Author-X-Name-First: Otto Author-X-Name-Last: Konstandatos Title: Two Exotic Lookback Options Abstract: This paper formally analyses two exotic options with lookback features, referred to as extreme spread lookback options and look-barrier options, first introduced by Bermin. The holder of such options receives partial protection from large price movements in the underlying, but at roughly the cost of a plain vanilla contract. This is achieved by increasing the leverage through either floating the strike price (for the case of extreme spread options) or introducing a partial barrier window (for the case of look-barrier options). We show how to statically replicate the prices of these hybrid exotic derivatives with more elementary European binary options and their images, using new methods first introduced by Buchen and Konstandatos. These methods allow considerable simplification in the analysis, leading to closed-form representations in the Black-Scholes framework. Journal: Applied Mathematical Finance Pages: 387-402 Issue: 4 Volume: 15 Year: 2008 Keywords: Exotic options, lookback options, barrier options, option pricing, method of images, X-DOI: 10.1080/13504860802012824 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802012824 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:387-402 Template-Type: ReDIF-Article 1.0 Author-Name: Rene Carmona Author-X-Name-First: Rene Author-X-Name-Last: Carmona Author-Name: Michael Ludkovski Author-X-Name-First: Michael Author-X-Name-Last: Ludkovski Title: Pricing Asset Scheduling Flexibility using Optimal Switching Abstract: We study the financial engineering aspects of operational flexibility of energy assets. The current practice relies on a representation that uses strips of European spark-spread options, ignoring the operational constraints. Instead, we propose a new approach based on a stochastic impulse control framework. The model reduces to a cascade of optimal stopping problems and directly demonstrates that the optimal dispatch policies can be described with the aid of 'switching boundaries', similar to the free boundaries of standard American options. Our main contribution is a new method of numerical solution relying on Monte Carlo regressions. The scheme uses dynamic programming to efficiently approximate the optimal dispatch policy along the simulated paths. Convergence analysis is carried out and results are illustrated with a variety of concrete computational examples. We benchmark and compare our scheme with alternative numerical methods. Journal: Applied Mathematical Finance Pages: 405-447 Issue: 5-6 Volume: 15 Year: 2008 Keywords: Optimal switching, Monte Carlo, operational flexibility, impulse control, Snell envelope, X-DOI: 10.1080/13504860802170507 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802170507 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:405-447 Template-Type: ReDIF-Article 1.0 Author-Name: Helyette Geman Author-X-Name-First: Helyette Author-X-Name-Last: Geman Title: INTRODUCTION Abstract: Journal: Applied Mathematical Finance Pages: 403-404 Issue: 5-6 Volume: 15 Year: 2008 X-DOI: 10.1080/13504860802379884 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802379884 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:403-404 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel Hikspoors Author-X-Name-First: Samuel Author-X-Name-Last: Hikspoors Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Asymptotic Pricing of Commodity Derivatives using Stochastic Volatility Spot Models Abstract: It is well known that stochastic volatility is an essential feature of commodity spot prices. By using methods of singular perturbation theory, we obtain approximate but explicit closed-form pricing equations for forward contracts and options on single- and two-name forward prices. The expansion methodology is based on a fast mean-reverting stochastic volatility driving factor and leads to pricing results in terms of constant volatility prices, their Deltas and their Delta-Gammas. Both the standard single-factor mean-reverting spot model and a two-factor generalization, in which the long-run mean is itself mean-reverting, are extended to include stochastic volatility and each is analysed in detail. The stochastic volatility corrections can be used to efficiently calibrate option prices and compute sensitivities. Journal: Applied Mathematical Finance Pages: 449-477 Issue: 5-6 Volume: 15 Year: 2008 Keywords: Commodity derivatives, stochastic volatility, spread options, singular perturbation methods, X-DOI: 10.1080/13504860802170432 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802170432 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:449-477 Template-Type: ReDIF-Article 1.0 Author-Name: Mats Kjaer Author-X-Name-First: Mats Author-X-Name-Last: Kjaer Title: Pricing of Swing Options in a Mean Reverting Model with Jumps Abstract: We investigate the pricing of swing options in a model where the logarithm of the spot price is the sum of a deterministic seasonal trend and an Ornstein-Uhlenbeck process driven by a jump diffusion. First we calibrate the model to Nord Pool electricity market data. Second, the existence of an optimal exercise strategy is proved, and we present a numerical algorithm for computation of the swing option prices. It involves dynamic programming and the solution of multiple parabolic partial integro-differential equations by finite differences. Numerical results show that adding jumps to a diffusion may result in 2-35% higher swing option prices, depending on the moneyness and timing flexibility of the option. Journal: Applied Mathematical Finance Pages: 479-502 Issue: 5-6 Volume: 15 Year: 2008 Keywords: Energy derivatives, swing options, jump diffusions, parabolic PIDEs, finite differences, X-DOI: 10.1080/13504860802170556 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802170556 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:479-502 Template-Type: ReDIF-Article 1.0 Author-Name: E. Nasakkala Author-X-Name-First: E. Author-X-Name-Last: Nasakkala Author-Name: J. Keppo Author-X-Name-First: J. Author-X-Name-Last: Keppo Title: Hydropower with Financial Information Abstract: The paper considers a single utility company's long- and medium-term hydropower planning. The uncertainties are from the electricity forward curve and a random inflow. A simple and intuitive parameterization is given for the optimal production strategy. The accuracy of the parameterization is analysed by comparing its expected cash flows with the corresponding upper bound. In a test case the proposed method is compared with the realized production strategy of a Norwegian hydropower producer during winters 1997-2003. The parameterization gives earnings that are within 2.6% from the theoretical upper bound. Further, the results illustrate that during some years, part of the realized production strategy can be explained with the method, suggesting that during these years the forward curve information has already been incorporated in the production planning. However, even during the years when the correlation between the proposed strategy and the realized production is low, the strategy would have increased the realized earnings. This suggests that the information from the derivative markets would improve the production strategy. Journal: Applied Mathematical Finance Pages: 503-529 Issue: 5-6 Volume: 15 Year: 2008 Keywords: Electricity forward curve, hydropower production, X-DOI: 10.1080/13504860701852494 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701852494 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:503-529 Template-Type: ReDIF-Article 1.0 Author-Name: Helyette Geman Author-X-Name-First: Helyette Author-X-Name-Last: Geman Author-Name: Stelios Kourouvakalis Author-X-Name-First: Stelios Author-X-Name-Last: Kourouvakalis Title: A Lattice-Based Method for Pricing Electricity Derivatives Under the Threshold Model Abstract: Of the several models introduced for the modelling of electricity prices, the one proposed by Geman and Roncoroni, that we will refer to as the 'threshold model', has exhibited significant success in both its statistical properties and ability to accurately replicate trajectories of electricity prices. This article presents a lattice-based method for the discretization of the threshold model that allows for the pricing of derivatives, including swing options. The methodology builds on an idea presented by Bally et al. for discretizing density functions, and constructs an approximating process that is shown to be a good proxy of the original process, producing a grid that incorporates both mean reversion and jumps. Journal: Applied Mathematical Finance Pages: 531-567 Issue: 5-6 Volume: 15 Year: 2008 Keywords: Electricity spot prices, threshold model, lattice-based jump representation, X-DOI: 10.1080/13504860802379835 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802379835 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:15:y:2008:i:5-6:p:531-567 Template-Type: ReDIF-Article 1.0 Author-Name: Robert Elliott Author-X-Name-First: Robert Author-X-Name-Last: Elliott Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Title: On Markov-modulated Exponential-affine Bond Price Formulae Abstract: We consider the bond valuation problem when the short rate process is described by a Markovian regime-switching Hull-White model or a Markovian regime-switching Cox-Ingersoll-Ross model. In each of the two short rate models, we establish a Markov-modulated exponential-affine bond price formula with coefficients given in terms of fundamental matrix solutions of linear matrix differential equations. Journal: Applied Mathematical Finance Pages: 1-15 Issue: 1 Volume: 16 Year: 2009 Keywords: Exponential affine form, bond valuation, regime-switching forward measure, fundamental matrix solution, X-DOI: 10.1080/13504860802015744 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802015744 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:1:p:1-15 Template-Type: ReDIF-Article 1.0 Author-Name: Luca Vincenzo Ballestra Author-X-Name-First: Luca Vincenzo Author-X-Name-Last: Ballestra Author-Name: Graziella Pacelli Author-X-Name-First: Graziella Author-X-Name-Last: Pacelli Title: A Numerical Method to Price Defaultable Bonds Based on the Madan and Unal Credit Risk Model Abstract: We propose a numerical method to price corporate bonds based on the model of default risk developed by Madan and Unal. Using a perturbation approach, we derive two semi-explicit formulae that allow us to approximate the survival probability of the firm issuing the bond very efficiently. More precisely, we consider both the first- and second-order power series expansions of the survival probability in powers of the model parameter c. The zero-order coefficient of the series is evaluated using an exact analytical formula. The first- and second-order coefficients of the series are computed using an approximation algorithm based on the Laplace transform. Extensive simulation is carried out on several test cases where the parameters of the model of Madan and Unal are chosen from Grundke and Riedel, and bonds with different maturities are considered. The numerical experiments performed reveal that the numerical method proposed in this paper is accurate and computationally efficient. Journal: Applied Mathematical Finance Pages: 17-36 Issue: 1 Volume: 16 Year: 2009 Keywords: Credit risk, defaultable bonds, asymptotic expansion, X-DOI: 10.1080/13504860802091240 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802091240 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:1:p:17-36 Template-Type: ReDIF-Article 1.0 Author-Name: Carl Chiarella Author-X-Name-First: Carl Author-X-Name-Last: Chiarella Author-Name: Andrew Ziogas Author-X-Name-First: Andrew Author-X-Name-Last: Ziogas Title: American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach Abstract: We consider the American option pricing problem in the case where the underlying asset follows a jump-diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro-partial differential equation (IPDE) on a region restricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on an unrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE in the case of a call option on a dividend paying underlying to obtain the solution in the form of a pair of linked integral equations for the free boundary and the option price. We also derive new results concerning the limit for the free boundary at expiry. Finally, we present a numerical algorithm for the solution of the linked integral equation system for the American call price, its delta and the early exercise boundary. We use the numerical results to quantify the impact of jumps on American call prices and the early exercise boundary. Journal: Applied Mathematical Finance Pages: 37-79 Issue: 1 Volume: 16 Year: 2009 Keywords: American options, jump-diffusion, Volterra integral equation, free boundary problem, Fourier transform, X-DOI: 10.1080/13504860802221672 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802221672 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:1:p:37-79 Template-Type: ReDIF-Article 1.0 Author-Name: Sergio Ortobelli Author-X-Name-First: Sergio Author-X-Name-Last: Ortobelli Author-Name: Svetlozar Rachev Author-X-Name-First: Svetlozar Author-X-Name-Last: Rachev Author-Name: Haim Shalit Author-X-Name-First: Haim Author-X-Name-Last: Shalit Author-Name: Frank Fabozzi Author-X-Name-First: Frank Author-X-Name-Last: Fabozzi Title: Orderings and Probability Functionals Consistent with Preferences Abstract: This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First, we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors' preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally, we show how we can use risk measures and orderings consistent with some preferences to determine the investors' optimal choices. Journal: Applied Mathematical Finance Pages: 81-102 Issue: 1 Volume: 16 Year: 2009 Keywords: G11, C44, C61, X-DOI: 10.1080/13504860802327180 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802327180 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:1:p:81-102 Template-Type: ReDIF-Article 1.0 Author-Name: Olivier Bardou Author-X-Name-First: Olivier Author-X-Name-Last: Bardou Author-Name: Sandrine Bouthemy Author-X-Name-First: Sandrine Author-X-Name-Last: Bouthemy Author-Name: Gilles Pages Author-X-Name-First: Gilles Author-X-Name-Last: Pages Title: Optimal Quantization for the Pricing of Swing Options Abstract: In this paper we investigate a numerical algorithm for the pricing of swing options, relying on the so-called optimal quantization method. The numerical procedure is described in detail and numerous simulations are provided to assert its efficiency. In particular, we carry out a comparison with the Longstaff-Schwartz algorithm. Journal: Applied Mathematical Finance Pages: 183-217 Issue: 2 Volume: 16 Year: 2009 Keywords: Swing options, stochastic control, optimal quantization, energy, X-DOI: 10.1080/13504860802453218 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802453218 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:2:p:183-217 Template-Type: ReDIF-Article 1.0 Author-Name: Alvaro Cartea Author-X-Name-First: Alvaro Author-X-Name-Last: Cartea Author-Name: Marcelo Figueroa Author-X-Name-First: Marcelo Author-X-Name-Last: Figueroa Author-Name: Helyette Geman Author-X-Name-First: Helyette Author-X-Name-Last: Geman Title: Modelling Electricity Prices with Forward Looking Capacity Constraints Abstract: We present a spot price model for wholesale electricity prices which incorporates forward looking information that is available to all market players. We focus on information that measures the extent to which the capacity of the England and Wales generation park will be constrained over the next 52 weeks. We propose a measure of 'tight market conditions', based on capacity constraints, which identifies the weeks of the year when price spikes are more likely to occur. We show that the incorporation of this type of forward looking information, not uncommon in electricity markets, improves the modelling of spikes (timing and magnitude) and the different speeds of mean reversion. Journal: Applied Mathematical Finance Pages: 103-122 Issue: 2 Volume: 16 Year: 2009 Keywords: Capacity constraints, mean reversion, electricity indicated demand, electricity indicated generation, regime switching model, X-DOI: 10.1080/13504860802351164 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802351164 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:2:p:103-122 Template-Type: ReDIF-Article 1.0 Author-Name: James Primbs Author-X-Name-First: James Author-X-Name-Last: Primbs Author-Name: Muruhan Rathinam Author-X-Name-First: Muruhan Author-X-Name-Last: Rathinam Title: Trader Behavior and its Effect on Asset Price Dynamics Abstract: In this paper, we present a natural mathematical framework to model trader behavior as a continuous time discrete event process, and derive stochastic differential equations for aggregate behavior and price dynamics by passing to diffusion limits. In particular, we model extraneous, value, momentum and hedge traders. Through analysis and numerical simulation we explore some of the effects these trading strategies have on price dynamics. Journal: Applied Mathematical Finance Pages: 151-181 Issue: 2 Volume: 16 Year: 2009 Keywords: Trader behavior, price dynamics, stock pinning, diffusion limit, Poisson random measure, X-DOI: 10.1080/13504860802583444 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802583444 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:2:p:151-181 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Zanger Author-X-Name-First: Daniel Author-X-Name-Last: Zanger Title: Convergence of a Least-Squares Monte Carlo Algorithm for Bounded Approximating Sets Abstract: We analyse the convergence properties of the Longstaff-Schwartz algorithm for approximately solving optimal stopping problems that arise in the pricing of American (Bermudan) financial options. Based on a new approximate dynamic programming principle error propagation inequality, we prove sample complexity error estimates for this algorithm for the case in which the corresponding approximation spaces may not necessarily possess any linear structure at all and may actually be any arbitrary sets of functions, each of which is uniformly bounded and possesses finite VC-dimension, but is not required to satisfy any further material conditions. In particular, we do not require that the approximation spaces be convex or closed, and we thus significantly generalize the results of Egloff, Clement et al., and others. Using our error estimation theorems, we also prove convergence, up to any desired probability, of the algorithm for approximating sets defined using L2 orthonormal bases, within a framework depending subexponentially on the number of time steps. In addition, we prove estimates on the overall convergence rate of the algorithm for approximation spaces defined by polynomials. Journal: Applied Mathematical Finance Pages: 123-150 Issue: 2 Volume: 16 Year: 2009 Keywords: Least-squares Monte Carlo, Longstaff-Schwartz algorithm, American options, optimal stopping, statistical learning, X-DOI: 10.1080/13504860802516881 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802516881 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:2:p:123-150 Template-Type: ReDIF-Article 1.0 Author-Name: Koichi Matsumoto Author-X-Name-First: Koichi Author-X-Name-Last: Matsumoto Title: Mean-Variance Hedging with Uncertain Trade Execution Abstract: This paper studies a hedging problem of a contingent claim in a discrete time model. The contingent claim is hedged by one illiquid risky asset and the hedging error is measured by a quadratic criterion. In our model, trade does not always succeed and then trade times are not only discrete, but also random. The uncertainty of trade execution represents the liquidity risk. First we find an optimal hedging strategy with fixed initial condition. Next we consider an optimal initial condition. Finally, we study a binomial model as a simple example. Journal: Applied Mathematical Finance Pages: 219-252 Issue: 3 Volume: 16 Year: 2009 Keywords: Hedging, derivatives, execution risk, X-DOI: 10.1080/13504860802583972 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802583972 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:219-252 Template-Type: ReDIF-Article 1.0 Author-Name: Erik Ekstrom Author-X-Name-First: Erik Author-X-Name-Last: Ekstrom Author-Name: Per Lotstedt Author-X-Name-First: Per Author-X-Name-Last: Lotstedt Author-Name: Johan Tysk Author-X-Name-First: Johan Author-X-Name-Last: Tysk Title: Boundary Values and Finite Difference Methods for the Single Factor Term Structure Equation Abstract: We study the classical single factor term structure equation for models that predict non-negative interest rates. For these models we develop a fast and accurate finite difference method (FD) using the appropriate boundary conditions at zero. Journal: Applied Mathematical Finance Pages: 253-259 Issue: 3 Volume: 16 Year: 2009 Keywords: Term structure equation, degenerate parabolic equations, stochastic representation, finite difference method, X-DOI: 10.1080/13504860802584004 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802584004 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:253-259 Template-Type: ReDIF-Article 1.0 Author-Name: Jaehyuk Choi Author-X-Name-First: Jaehyuk Author-X-Name-Last: Choi Author-Name: Kwangmoon Kim Author-X-Name-First: Kwangmoon Author-X-Name-Last: Kim Author-Name: Minsuk Kwak Author-X-Name-First: Minsuk Author-X-Name-Last: Kwak Title: Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion Abstract: We provide an accurate approximation method for inverting an option price to the implied volatility under arithmetic Brownian motion, which is widely quoted in Fixed Income markets. The maximum error in the volatility is in the order of 10-10 of the given option price and much smaller for the near-the-money options. Thus our approximation can be used as an exact solution without further refinements of iterative methods. Journal: Applied Mathematical Finance Pages: 261-268 Issue: 3 Volume: 16 Year: 2009 Keywords: Normal implied volatility, basis point volatility, arithmetic Brownian motion, rational approximation, closed form approximation, X-DOI: 10.1080/13504860802583436 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802583436 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:261-268 Template-Type: ReDIF-Article 1.0 Author-Name: Simona Svoboda-Greenwood Author-X-Name-First: Simona Author-X-Name-Last: Svoboda-Greenwood Title: Displaced Diffusion as an Approximation of the Constant Elasticity of Variance Abstract: The CEV (constant elasticity of variance) and displaced diffusion processes have been posited as suitable alternatives to a lognormal process in modelling the dynamics of market variables such as stock prices and interest rates. Marris (1999) noted that, for a certain parameterization, option prices produced by the two processes display close correspondence across a range of strikes and maturities. This parametrization is a simple linearization of the CEV dynamics around the initial value of the underlying and we quantify the observed agreement in option prices by performing a small time expansion of the option prices around the forward-at-the-money value of the underlying. We show further results regarding the comparability of the conditional probability density functions of the two processes and hence the associated moments. Journal: Applied Mathematical Finance Pages: 269-286 Issue: 3 Volume: 16 Year: 2009 Keywords: Constant elasticity of variance (CEV), displaced diffusion, option pricing, asymptotic expansions, X-DOI: 10.1080/13504860802628553 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802628553 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:269-286 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Egloff Author-X-Name-First: Daniel Author-X-Name-Last: Egloff Author-Name: Markus Leippold Author-X-Name-First: Markus Author-X-Name-Last: Leippold Title: The Valuation of American Options with Stochastic Stopping Time Constraints Abstract: This paper concerns the pricing of American options with stochastic stopping time constraints expressed in terms of the states of a Markov process. Following the ideas of Menaldi et al., we transform the constrained into an unconstrained optimal stopping problem. The transformation replaces the original payoff by the value of a generalized barrier option. We also provide a Monte Carlo method to numerically calculate the option value for multidimensional Markov processes. We adapt the Longstaff-Schwartz algorithm to solve the stochastic Cauchy-Dirichlet problem related to the valuation problem of the barrier option along a set of simulated trajectories of the underlying Markov process. Journal: Applied Mathematical Finance Pages: 287-305 Issue: 3 Volume: 16 Year: 2009 Keywords: American options, optimal stopping under constraints, Feller process, out-performance options, management options, Monte Carlo simulation, X-DOI: 10.1080/13504860802645706 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802645706 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:287-305 Template-Type: ReDIF-Article 1.0 Author-Name: Umberto Cherubini Author-X-Name-First: Umberto Author-X-Name-Last: Cherubini Author-Name: Silvia Romagnoli Author-X-Name-First: Silvia Author-X-Name-Last: Romagnoli Title: Computing the Volume of n-Dimensional Copulas Abstract: A problem that is very relevant in applications of copula functions to finance is the computation of the survival copula, which is applied to enforce multivariate put-call parity. This may be very complex for large dimensions. The problem is a special case of the more general problem of volume computation in high-dimensional copulas. We provide an algorithm for the exact computation of the volume of copula functions in cases where the copula function is computable in closed form. We apply the algorithm to the problem of computing the survival of a copula function in the pricing problem of a multivariate digital option, and we provide evidence that this is feasible for baskets of up to 20 underlying assets, with acceptable CPU time performance. Journal: Applied Mathematical Finance Pages: 307-314 Issue: 4 Volume: 16 Year: 2009 Keywords: Copula functions, copula volume, multivariate options, computational pricing methods, X-DOI: 10.1080/13504860802597311 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802597311 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:4:p:307-314 Template-Type: ReDIF-Article 1.0 Author-Name: Steven Vanduffel Author-X-Name-First: Steven Author-X-Name-Last: Vanduffel Author-Name: Andrew Chernih Author-X-Name-First: Andrew Author-X-Name-Last: Chernih Author-Name: Matheusz Maj Author-X-Name-First: Matheusz Author-X-Name-Last: Maj Author-Name: Wim Schoutens Author-X-Name-First: Wim Author-X-Name-Last: Schoutens Title: A Note on the Suboptimality of Path-Dependent Pay-Offs in Levy Markets Abstract: Cox and Leland used techniques from the field of stochastic control theory to show that, in the particular case of a Brownian motion for the asset log-returns, risk-averse decision makers with a fixed investment horizon prefer path-independent pay-offs over path-dependent pay-offs. In this note we provide a novel and simple proof for the Cox and Leland result and we will extend it to general Levy markets where pricing is based on the Esscher transform (exponential tilting). It is also shown that, in these markets, optimal path-independent pay-offs are increasing with the underlying final asset value. We provide examples that allow explicit verification of our theoretical findings and also show that the inefficiency cost of path-dependent pay-offs can be significant. Our results indicate that path-dependent investment pay-offs, the use of which is widespread in financial markets, do not offer good value from the investor's point of view. Journal: Applied Mathematical Finance Pages: 315-330 Issue: 4 Volume: 16 Year: 2009 Keywords: Path-dependent pay-offs, Levy markets, X-DOI: 10.1080/13504860802639360 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802639360 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:4:p:315-330 Template-Type: ReDIF-Article 1.0 Author-Name: Jungmin Choi Author-X-Name-First: Jungmin Author-X-Name-Last: Choi Author-Name: Mattias Jonsson Author-X-Name-First: Mattias Author-X-Name-Last: Jonsson Title: Partial Hedging in Financial Markets with a Large Agent Abstract: We investigate the partial hedging problem in financial markets with a large agent. An agent is said to be large if his/her trades influence the equilibrium price. We develop a stochastic differential equation (SDE) with a single large agent parameter to model such a market. We focus on minimizing the expected value of the size of the shortfall in the large agent model. A Bellman-type partial differential equation (PDE) is derived, and the Legendre transform is used to consider the dual shortfall function. An asymptotic analysis leads us to conclude that the shortfall function (expected loss) increases when there is a large agent, which means that one would need more capital to hedge away risk in the market with a large agent. This asymptotic analysis is confirmed by performing Monte Carlo simulations. Journal: Applied Mathematical Finance Pages: 331-346 Issue: 4 Volume: 16 Year: 2009 Keywords: Partial hedging, large agent, Bellman PDE, X-DOI: 10.1080/13504860802670191 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802670191 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:4:p:331-346 Template-Type: ReDIF-Article 1.0 Author-Name: Chris Anderson Author-X-Name-First: Chris Author-X-Name-Last: Anderson Author-Name: Neil Brisley Author-X-Name-First: Neil Author-X-Name-Last: Brisley Title: Employee Stock Options: An Up-and-Out Protected Barrier Call Abstract: A well-known numerical lattice model, widely used to value employee stock options (ESOs), can be interpreted as a variation on the up-and-out protected barrier call, a version of which is valued in closed form by Carr (1995). We clarify that valuation formula and extend it to take account of the reality of possible vesting date exercise by employees. Journal: Applied Mathematical Finance Pages: 347-352 Issue: 4 Volume: 16 Year: 2009 Keywords: Employee stock options, up-and-out protected barrier call, X-DOI: 10.1080/13504860902753251 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860902753251 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:4:p:347-352 Template-Type: ReDIF-Article 1.0 Author-Name: Evan Papageorgiou Author-X-Name-First: Evan Author-X-Name-Last: Papageorgiou Author-Name: Ronnie Sircar Author-X-Name-First: Ronnie Author-X-Name-Last: Sircar Title: Multiscale Intensity Models and Name Grouping for Valuation of Multi-Name Credit Derivatives Abstract: The pricing of collateralized debt obligations (CDOs) and other basket credit derivatives is contingent upon (i) a realistic modelling of the firms' default times and the correlation between them, and (ii) efficient computational methods for computing the portfolio loss distribution from the individual firms' default time distributions. Factor models, a widely used class of pricing models, are computationally tractable despite the large dimension of the pricing problem, thus satisfying issue (ii), but to have any hope of calibrating CDO data, numerically intense versions of these models are required. We revisit the intensity-based modelling setup for basket credit derivatives and, with the aforementioned issues in mind, we propose improvements (a) via incorporating fast mean-reverting stochastic volatility in the default intensity processes, and (b) by considering homogeneous groups within the original set of firms. This can be thought of as a hybrid of top-down and bottom-up approaches. We present a calibration example, including data in the midst of the 2008 financial credit crisis, and discuss the relative performance of the framework. Journal: Applied Mathematical Finance Pages: 353-383 Issue: 4 Volume: 16 Year: 2009 Keywords: Collateralized debt obligations, intensity-based model, stochastic volatility, asymptotic approximation, multiple time scales, homogeneous-group factor models, bottom-up, top-down, X-DOI: 10.1080/13504860902765545 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860902765545 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:4:p:353-383 Template-Type: ReDIF-Article 1.0 Author-Name: Kurt Jornsten Author-X-Name-First: Kurt Author-X-Name-Last: Jornsten Author-Name: Jan Ubøe Author-X-Name-First: Jan Author-X-Name-Last: Ubøe Title: Strategic Pricing of Commodities Abstract: We consider a setting where a large number of agents are trading commodity bundles. Assuming that agents of the same type have a certain utility attached to each transaction, we construct a statistical equilibrium which in turn implies prices on the different commodities. Our basic question is then the following. Assuming that some commodities come out with prices that are socially unacceptable, is it possible to change these prices systematically if a new type of agent is paid to enter the market? We will consider explicit examples where this can be done. Journal: Applied Mathematical Finance Pages: 385-399 Issue: 5 Volume: 16 Year: 2009 Keywords: Agent preferences, efficient markets, statistical equilibria, commodity prices, arbitrageurs, X-DOI: 10.1080/13504860802639261 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860802639261 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:5:p:385-399 Template-Type: ReDIF-Article 1.0 Author-Name: Andreas Kolbe Author-X-Name-First: Andreas Author-X-Name-Last: Kolbe Author-Name: Rudi Zagst Author-X-Name-First: Rudi Author-X-Name-Last: Zagst Title: Valuation of Mortgage-Backed Securities and Mortgage Derivatives: A Closed-Form Approximation Abstract: In this paper we develop a closed-form and thus computationally highly efficient formula to approximate the value of fixed-rate mortgage-backed securities (MBS). Our modelling framework is based on reduced-form and prepayment-risk-neutral valuation techniques and offers two major extensions compared with existing closed-form approximation approaches: we include a stochastic baseline prepayment factor in our model and we are able to capture the usual S-shaped curve of the refinancing incentive by a piecewise linear approximation. We apply our model to GNMA pass-through securities and test it on a 10-year sample of monthly GNMA MBS market prices for a wide range of coupons. Journal: Applied Mathematical Finance Pages: 401-427 Issue: 5 Volume: 16 Year: 2009 Keywords: Mortgage-backed security, prepayment, closed-form, risk-neutral pricing, X-DOI: 10.1080/13504860902781419 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860902781419 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:5:p:401-427 Template-Type: ReDIF-Article 1.0 Author-Name: Erhan Bayraktar Author-X-Name-First: Erhan Author-X-Name-Last: Bayraktar Author-Name: Bo Yang Author-X-Name-First: Bo Author-X-Name-Last: Yang Title: Multi-Scale Time-Changed Birth Processes for Pricing Multi-Name Credit Derivatives Abstract: We develop two parsimonious models for pricing multi-name credit derivatives. We derive closed form expression for the loss distribution, which then can be used in determining the prices of tranche and index swaps and more exotic derivatives on these contracts. Our starting point is the model of Ding et al., 2008, which takes the loss process as a time-changed birth process. We introduce stochastic parameter variations into the intensity of the loss process and use the multi-time scale approach of Fouque et al., 2003 and obtain explicit perturbation approximations to the loss distribution. We demonstrate the competence of our approach by calibrating it to the CDX index data. Journal: Applied Mathematical Finance Pages: 429-449 Issue: 5 Volume: 16 Year: 2009 Keywords: Pricing multi-name credit derivatives, pertubation approximation, multiple time scales, time-changed birth processes, index/tranche swap, calibration, X-DOI: 10.1080/13504860903073774 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903073774 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:5:p:429-449 Template-Type: ReDIF-Article 1.0 Author-Name: A. C. Belanger Author-X-Name-First: A. C. Author-X-Name-Last: Belanger Author-Name: P. A. Forsyth Author-X-Name-First: P. A. Author-X-Name-Last: Forsyth Author-Name: G. Labahn Author-X-Name-First: G. Author-X-Name-Last: Labahn Title: Valuing the Guaranteed Minimum Death Benefit Clause with Partial Withdrawals Abstract: In this paper, we give a method for computing the fair insurance fee associated with the guaranteed minimum death benefit (GMDB) clause included in many variable annuity contracts. We allow for partial withdrawals, a common feature in most GMDB contracts, and determine how this affects the GMDB fair insurance charge. Our method models the GMDB pricing problem as an impulse control problem. The resulting quasi-variational inequality is solved numerically using a fully implicit penalty method. The numerical results are obtained under both constant volatility and regime-switching models. A complete analysis of the numerical procedure is included. We show that the discrete equations are stable, monotone and consistent and hence obtain convergence to the unique, continuous viscosity solution, assuming this exists. Our results show that the addition of the partial withdrawal feature significantly increases the fair insurance charge for GMDB contracts. Journal: Applied Mathematical Finance Pages: 451-496 Issue: 6 Volume: 16 Year: 2009 Keywords: Variable annuities, guaranteed minimum death benefit (GMDB), viscosity solution, impulse control, fully implicit penalty method, X-DOI: 10.1080/13504860903075464 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075464 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:6:p:451-496 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Buchen Author-X-Name-First: Peter Author-X-Name-Last: Buchen Author-Name: Otto Konstandatos Author-X-Name-First: Otto Author-X-Name-Last: Konstandatos Title: A New Approach to Pricing Double-Barrier Options with Arbitrary Payoffs and Exponential Boundaries Abstract: We consider in this article the arbitrage free pricing of double knock-out barrier options with payoffs that are arbitrary functions of the underlying asset, where we allow exponentially time-varying barrier levels in an otherwise standard Black-Scholes model. Our approach, reminiscent of the method of images of electromagnetics, considerably simplifies the derivation of analytical formulae for this class of exotics by reducing the pricing of any double-barrier problem to that of pricing a related European option. We illustrate the method by reproducing the well-known formulae of Kunitomo and Ikeda (1992) for the standard knock-out double-barrier call and put options. We give an explanation for the rapid rate of convergence of the doubly infinite sums for affine payoffs in the stock price, as encountered in the pricing of double-barrier call and put options first observed by Kunitomo and Ikeda (1992). Journal: Applied Mathematical Finance Pages: 497-515 Issue: 6 Volume: 16 Year: 2009 Keywords: Exotic options, double-barrier options, method of images, parity relations of double-barrier options, X-DOI: 10.1080/13504860903075480 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075480 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:6:p:497-515 Template-Type: ReDIF-Article 1.0 Author-Name: Carlos Veiga Author-X-Name-First: Carlos Author-X-Name-Last: Veiga Author-Name: Uwe Wystup Author-X-Name-First: Uwe Author-X-Name-Last: Wystup Title: Closed Formula for Options with Discrete Dividends and Its Derivatives Abstract: We present a closed pricing formula for European options under the Black-Scholes model as well as formulas for its partial derivatives. The formulas are developed making use of Taylor series expansions and a proposition that relates expectations of partial derivatives with partial derivatives themselves. The closed formulas are attained assuming the dividends are paid in any state of the world. The results are readily extensible to time-dependent volatility models. For completeness, we reproduce the numerical results in Vellekoop and Nieuwenhuis, covering calls and puts, together with results on their partial derivatives. The closed formulas presented here allow a fast calculation of prices or implied volatilities when compared with other valuation procedures that rely on numerical methods. Journal: Applied Mathematical Finance Pages: 517-531 Issue: 6 Volume: 16 Year: 2009 Keywords: Equity option, discrete dividend, hedging, analytic formula, closed formula, X-DOI: 10.1080/13504860903075498 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075498 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:16:y:2009:i:6:p:517-531 Template-Type: ReDIF-Article 1.0 Author-Name: Dirk Becherer Author-X-Name-First: Dirk Author-X-Name-Last: Becherer Author-Name: Ian Ward Author-X-Name-First: Ian Author-X-Name-Last: Ward Title: Optimal Weak Static Hedging of Equity and Credit Risk Using Derivatives Abstract: We develop a generic method for constructing a weak static minimum variance hedge for a wide range of derivatives that may involve optimal exercise features or contingent cash flow streams to provide a hedge along a sequence of future hedging dates. The optimal hedge is constructed using a portfolio of pre-selected hedge instruments, which could be derivatives with different maturities. The hedge portfolio is weakly static in that it is initiated at time zero, does not involve intermediate re-balancing, but hedges may be gradually unwound over time. We study the static hedging of a convertible bond to demonstrate the method by an example that involves equity and credit risk. We investigate the robustness of the hedge performance with respect to parameter and model risk by numerical experiments. Journal: Applied Mathematical Finance Pages: 1-28 Issue: 1 Volume: 17 Year: 2010 Keywords: Static hedging, minimum variance hedging, displaced diffusion, stochastic volatility, calibration, convertible bond, X-DOI: 10.1080/13504860903075522 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075522 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:1:p:1-28 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Kohlmann Author-X-Name-First: Michael Author-X-Name-Last: Kohlmann Author-Name: Dewen Xiong Author-X-Name-First: Dewen Author-X-Name-Last: Xiong Author-Name: Zhongxing Ye Author-X-Name-First: Zhongxing Author-X-Name-Last: Ye Title: Mean Variance Hedging in a General Jump Model Abstract: We consider the mean-variance hedging of a contingent claim H when the discounted price process S is an [image omitted]-valued quasi-left continuous semimartingale with bounded jumps. We relate the variance-optimal martingale measure (VOMM) to a backward semimartingale equation (BSE) and show that the VOMM is equivalent to the original measure P if and only if the BSE has a solution. For a general contingent claim, we derive an explicit solution of the optimal strategy and the optimal cost of the mean-variance hedging by means of another BSE and an appropriate predictable process δ Journal: Applied Mathematical Finance Pages: 29-57 Issue: 1 Volume: 17 Year: 2010 Keywords: Mean-variance hedging, variance-optimal martingale measure, backward semimartingale equations, X-DOI: 10.1080/13504860903075605 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075605 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:1:p:29-57 Template-Type: ReDIF-Article 1.0 Author-Name: Pascal Heider Author-X-Name-First: Pascal Author-X-Name-Last: Heider Title: Numerical Methods for Non-Linear Black-Scholes Equations Abstract: In recent years non-linear Black-Scholes models have been used to build transaction costs, market liquidity or volatility uncertainty into the classical Black-Scholes concept. In this article we discuss the applicability of implicit numerical schemes for the valuation of contingent claims in these models. It is possible to derive sufficient conditions, which are required to ensure the convergence of the backward differentiation formula (BDF) and Crank-Nicolson scheme (CN) scheme to the unique viscosity solution. These stability conditions can be checked a priori and convergent schemes can be constructed for a large class of non-linear models and payoff profiles. However, if these conditions are not satisfied we show that the schemes are not convergent or produce spurious solutions. We study the practical implications of the derived stability criterions on relevant numerical examples. Journal: Applied Mathematical Finance Pages: 59-81 Issue: 1 Volume: 17 Year: 2010 Keywords: Non-linear Black-Scholes equation, BDF methods, fully implicit, viscosity solution, X-DOI: 10.1080/13504860903075670 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075670 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:1:p:59-81 Template-Type: ReDIF-Article 1.0 Author-Name: Ernst Eberlein Author-X-Name-First: Ernst Author-X-Name-Last: Eberlein Author-Name: Dilip Madan Author-X-Name-First: Dilip Author-X-Name-Last: Madan Title: Short Positions, Rally Fears and Option Markets Abstract: Index option pricing on world market indices are investigated using Levy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a rally before a crash. Three models are used to effectively calibrate index options at an annual maturity, and it is observed that positive jumps may be needed for FTSE, N225 and HSI. Rally before a crash probabilities are shown to have fallen by 10 points after July 2007. Typical implied volatility curves for such models are also described and illustrated. They have smirks and never smile. Journal: Applied Mathematical Finance Pages: 83-98 Issue: 1 Volume: 17 Year: 2010 Keywords: Spectrally negative processes, implied volatility smiles, two-sided exit problems, X-DOI: 10.1080/13504860903075688 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075688 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:1:p:83-98 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Baldeaux Author-X-Name-First: Jan Author-X-Name-Last: Baldeaux Author-Name: Marek Rutkowski Author-X-Name-First: Marek Author-X-Name-Last: Rutkowski Title: Static Replication of Forward-Start Claims and Realized Variance Swaps Abstract: The goal of this work is to examine the static replication of path-dependent derivatives such as realized variance swaps, using more standard products such as forward-start binary (i.e. digital) double calls and puts. We first examine, following Carr and Madan (2002), the static replication of path-independent claims with continuous and discontinuous payoff functions. Subsequently, the static replication of forward-start claims with payoffs given by a bivariate function of finite variation is examined. We postulate that certain forward-start binary (or barrier) options are traded. The work concludes by an application of our general results to the static hedging of a realized variance swap with forward-start binary (or barrier) options. Journal: Applied Mathematical Finance Pages: 99-131 Issue: 2 Volume: 17 Year: 2010 Keywords: Static replication, realized variance swap, binary option, barrier option, X-DOI: 10.1080/13504860903075621 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903075621 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:2:p:99-131 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Becker Author-X-Name-First: Martin Author-X-Name-Last: Becker Title: Comment on 'Correcting for Simulation Bias in Monte Carlo Methods to Value Exotic Options in Models Driven by Levy Processes' by C. Ribeiro and N. Webber Abstract: Ribeiro and Webber (2006) propose a method to correct for simulation bias in the Monte Carlo valuation of options with pay-offs depending on the extreme value(s) of the underlying which is driven by a special Levy process, namely a normal inverse Gaussian (NIG) or a variance gamma (VG) process. The proposed method was already successfully used by Beaglehole et al. (1997) and El Babsiri and Noel (1998) when the underlying follows a Brownian motion. Unfortunately, Ribeiro and Webber, in their attempt to exploit well-known subordinator representations of NIG and VG processes, overlook the fact that these subordinator representations lead to discontinuous subordinators. Therefore their correction method 'overcorrects' the simulation bias by magnitudes, resulting in a much bigger simulation bias with reversed sign. We point out where the assumption of a continuous subordinator is implicitly used in the paper of Ribeiro and Webber (2006). Furthermore, by applying the unbiased Monte Carlo valuation approach for Barrier options under VG models of Becker (2009) to the barrier and lookback options considered in Ribeiro and Webber (2006), we show that the newly introduced simulation bias exceeds the corrected simulation bias by far. Journal: Applied Mathematical Finance Pages: 133-146 Issue: 2 Volume: 17 Year: 2010 Keywords: Bridge Monte Carlo methods, simulation bias, barrier options, NIG process, VG process, X-DOI: 10.1080/13504860903137538 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903137538 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:2:p:133-146 Template-Type: ReDIF-Article 1.0 Author-Name: Shane Miller Author-X-Name-First: Shane Author-X-Name-Last: Miller Author-Name: Eckhard Platen Author-X-Name-First: Eckhard Author-X-Name-Last: Platen Title: Real-World Pricing for a Modified Constant Elasticity of Variance Model Abstract: This paper considers a modified constant elasticity of variance (MCEV) model. This model uses the familiar constant elasticity of variance form for the volatility of the growth optimal portfolio (GOP) in a continuous market. It leads to a GOP that follows the power of a time-transformed squared Bessel process. This paper derives analytic real-world prices for zero-coupon bonds, instantaneous forward rates and options on the GOP that are both theoretically revealing and computationally efficient. In addition, the paper examines options on exchange prices and options on zero-coupon bonds under the MCEV model. The semi-analytic prices derived for options on zero-coupon bonds can subsequently be used to price interest rate caps and floors. Journal: Applied Mathematical Finance Pages: 147-175 Issue: 2 Volume: 17 Year: 2010 Keywords: Benchmark approach, real-world pricing, growth optimal portfolio, constant elasticity of variance, zero-coupon bonds, exchange prices, interest rate caps and floors, X-DOI: 10.1080/13504860903155035 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903155035 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:2:p:147-175 Template-Type: ReDIF-Article 1.0 Author-Name: Kiseop Lee Author-X-Name-First: Kiseop Author-X-Name-Last: Lee Author-Name: Yong Zeng Author-X-Name-First: Yong Author-X-Name-Last: Zeng Title: Risk Minimization for a Filtering Micromovement Model of Asset Price Abstract: The classical option hedging problems have mostly been studied under continuous-time or equally spaced discrete-time models, which ignore two important components in the actual price: random trading times and market microstructure noise. In this paper, we study optimal hedging strategies for European derivatives based on a filtering micromovement model of asset prices with the two commonly ignored characteristics. We employ the local risk-minimization criterion to develop optimal hedging strategies under full information. Then, we project the hedging strategies on the observed information to obtain hedging strategies under partial information. Furthermore, we develop a related nonlinear filtering technique under the minimal martingale measure for the computation of such hedging strategies. Journal: Applied Mathematical Finance Pages: 177-199 Issue: 2 Volume: 17 Year: 2010 Keywords: Risk minimization, Minimal martingale measure, Filtering, Counting process, High frequency data, X-DOI: 10.1080/13504860903259852 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903259852 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:2:p:177-199 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Doust Author-X-Name-First: Paul Author-X-Name-Last: Doust Title: Two Useful Techniques for Financial Modelling Problems Abstract: A technique for defining an N × N correlation matrix in terms of N - 1 parameters is presented, as well as a reliable method for parameterizing positive weights or probabilities that sum to 1. Journal: Applied Mathematical Finance Pages: 201-210 Issue: 3 Volume: 17 Year: 2010 Keywords: Financial modelling, X-DOI: 10.1080/13504860903257666 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903257666 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:3:p:201-210 Template-Type: ReDIF-Article 1.0 Author-Name: Ernst Eberlein Author-X-Name-First: Ernst Author-X-Name-Last: Eberlein Author-Name: Kathrin Glau Author-X-Name-First: Kathrin Author-X-Name-Last: Glau Author-Name: Antonis Papapantoleon Author-X-Name-First: Antonis Author-X-Name-Last: Papapantoleon Title: Analysis of Fourier Transform Valuation Formulas and Applications Abstract: The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in Levy and stochastic volatility models. Journal: Applied Mathematical Finance Pages: 211-240 Issue: 3 Volume: 17 Year: 2010 Keywords: Option valuation, Fourier transform, semimartingales, Levy processes, stochastic volatility models, options on several assets, X-DOI: 10.1080/13504860903326669 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903326669 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:3:p:211-240 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Forde Author-X-Name-First: Martin Author-X-Name-Last: Forde Author-Name: Antoine Jacquier Author-X-Name-First: Antoine Author-X-Name-Last: Jacquier Title: Robust Approximations for Pricing Asian Options and Volatility Swaps Under Stochastic Volatility Abstract: We show that if the discounted Stock price process is a continuous martingale, then there is a simple relationship linking the variance of the terminal Stock price and the variance of its arithmetic average. We use this to establish a model-independent upper bound for the price of a continuously sampled fixed-strike arithmetic Asian call option, in the presence of non-zero time-dependent interest rates (Theorem 1.2). We also propose a model-independent lognormal moment-matching procedure for approximating the price of an Asian call, and we show how to apply these approximations under the Black-Scholes and Heston models (subsection 1.3). We then apply a similar analysis to a time-dependent Heston stochastic volatility model, and we show how to construct a time-dependent mean reversion and volatility-of-variance function, so as to be consistent with the observed variance swap curve and a pre-specified term structure for the variance of the integrated variance (Theorem 2.1). We characterize the small-time asymptotics of the first and second moments of the integrated variance (Proposition 2.2) and derive an approximation for the price of a volatility swap under the time-dependent Heston model ( Equation (52)), using the Brockhaus-Long approximation (Brockhaus, and Long, 2000). We also outline a bootstrapping procedure for calibrating a piecewise-linear mean reversion level and volatility-of-volatility function (Subsection 2.3.2). Journal: Applied Mathematical Finance Pages: 241-259 Issue: 3 Volume: 17 Year: 2010 Keywords: Asian options, Heston, stochastic volatility, calibration, volatility swaps, X-DOI: 10.1080/13504860903335348 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903335348 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:3:p:241-259 Template-Type: ReDIF-Article 1.0 Author-Name: Fannu Hu Author-X-Name-First: Fannu Author-X-Name-Last: Hu Author-Name: Charles Knessl Author-X-Name-First: Charles Author-X-Name-Last: Knessl Title: Asymptotics of Barrier Option Pricing Under the CEV Process Abstract: We apply a singular perturbation analysis to some option pricing models. To illustrate the technique we first consider the European put option under the standard Black-Scholes model, with or without barriers. Then we consider the same option under the constant elasticity of variance (CEV) assumption, which is also called the square root process. In the CEV model the variability effects in the evolution of the asset, on which the option is based, are proportional to the square root of the asset value. We also consider the CEV model with barriers, and this leads to a rich asymptotic structure. The analysis assumes that the variability is small and employs the ray method of geometrical optics and matched asymptotic expansions. Journal: Applied Mathematical Finance Pages: 261-300 Issue: 3 Volume: 17 Year: 2010 Keywords: Barrier options, Black-Scholes model, CEV process, singular perturbation, X-DOI: 10.1080/13504860903335355 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903335355 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:3:p:261-300 Template-Type: ReDIF-Article 1.0 Author-Name: Reiichiro Kawai Author-X-Name-First: Reiichiro Author-X-Name-Last: Kawai Author-Name: Arturo Kohatsu-Higa Author-X-Name-First: Arturo Author-X-Name-Last: Kohatsu-Higa Title: Computation of Greeks and Multidimensional Density Estimation for Asset Price Models with Time-Changed Brownian Motion Abstract: The main purpose of this article is to propose computational methods for Greeks and the multidimensional density estimation for an asset price dynamics model defined with time-changed Brownian motions. Our approach is based on an application of the Malliavin integration-by-parts formula on the Gaussian space conditioning on the jump component. Some numerical examples are presented to illustrate the effectiveness of our results. Journal: Applied Mathematical Finance Pages: 301-321 Issue: 4 Volume: 17 Year: 2010 Keywords: Integration-by-parts formula, Malliavin calculus, normal inverse Gaussian process, time-changed Brownian motion, variance gamma process, X-DOI: 10.1080/13504860903336429 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903336429 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:4:p:301-321 Template-Type: ReDIF-Article 1.0 Author-Name: Colin Atkinson Author-X-Name-First: Colin Author-X-Name-Last: Atkinson Author-Name: Emmeline Storey Author-X-Name-First: Emmeline Author-X-Name-Last: Storey Title: Building an Optimal Portfolio in Discrete Time in the Presence of Transaction Costs Abstract: Portfolio theory covers different approaches to the construction of a portfolio offering maximum expected returns for a given level of risk tolerance where the goal is to find the optimal investment rule. Each investor has a certain utility for money which is reflected by the choice of a utility function. In this article, a risk averse power utility function is studied in discrete time for a large class of underlying probability distribution of the returns of the asset prices. Each investor chooses, at the beginning of an investment period, the feasible portfolio allocation which maximizes the expected value of the utility function for terminal wealth. Effects of both large and small proportional transaction costs on the choice of an optimal portfolio are taken into account. The transaction regions are approximated by using asymptotic methods when the proportional transaction costs are small and by using expansions about critical points for large transaction costs. Journal: Applied Mathematical Finance Pages: 323-357 Issue: 4 Volume: 17 Year: 2010 Keywords: Portfolio optimization, transaction costs, dynamic programming, utility maximization, X-DOI: 10.1080/13504860903336437 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903336437 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:4:p:323-357 Template-Type: ReDIF-Article 1.0 Author-Name: Luitgard Veraart Author-X-Name-First: Luitgard Author-X-Name-Last: Veraart Title: Optimal Market Making in the Foreign Exchange Market Abstract: This paper is concerned with optimal market making in the foreign exchange market. The market maker's holdings in the different currencies are modelled as stochastic processes that are influenced by both the stochastic exchange rates and the stochastic customer buy and sell orders. The market maker can control their own bid and ask price quotes and, additionally, can buy and sell at other market participants' quotes. The resulting stochastic control problem consists of a controlled diffusion problem for the optimal quotes and a singular control problem for optimal trades at other market participants' quotes. A Markov chain approximation is used to derive optimal strategies. Journal: Applied Mathematical Finance Pages: 359-372 Issue: 4 Volume: 17 Year: 2010 Keywords: Market making, optimal investment, proportional transaction costs, stochastic control, X-DOI: 10.1080/13504860903387588 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903387588 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:4:p:359-372 Template-Type: ReDIF-Article 1.0 Author-Name: Roger Lord Author-X-Name-First: Roger Author-X-Name-Last: Lord Title: Comment on: A Note on the Discontinuity Problem in Heston's Stochastic Volatility Model Abstract: Guo and Hung (2007) recently studied the complex logarithm present in the characteristic function of Heston's stochastic volatility model. They proposed an algorithm for the evaluation of the characteristic function that is claimed to preserve its continuity. We show their algorithm is correct, although their proof is not. Journal: Applied Mathematical Finance Pages: 373-376 Issue: 4 Volume: 17 Year: 2010 Keywords: Complex logarithm, stochastic volatility, Heston, characteristic function, X-DOI: 10.1080/13504860903387612 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903387612 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:4:p:373-376 Template-Type: ReDIF-Article 1.0 Author-Name: Thomas Kokholm Author-X-Name-First: Thomas Author-X-Name-Last: Kokholm Author-Name: Elisa Nicolato Author-X-Name-First: Elisa Author-X-Name-Last: Nicolato Title: Sato Processes in Default Modelling Abstract: In reduced form default models, the instantaneous default intensity is the classical modelling object. Survival probabilities are then given by the Laplace transform of the cumulative hazard defined as the integrated intensity process. Instead, recent literature tends to specify the cumulative hazard process directly. Within this framework we present a new model class where cumulative hazards are described by self-similar additive processes, also known as Sato processes. Furthermore, we analyse specifications obtained via a simple deterministic time change of a homogeneous Levy process. While the processes in these two classes share the same average behaviour over time, the associated intensities exhibit very different properties. Concrete specifications are calibrated to data on all the single names included in the iTraxx Europe index. The performances are compared with those of the classical Cox-Ingersoll-Ross intensity and a recently proposed class of intensity models based on Ornstein-Uhlenbeck-type processes. It is shown that the time-inhomogeneous Levy models achieve comparable calibration errors with fewer parameters and with more stable parameter estimates over time. However, the calibration performance of the Sato processes and the time-change specifications are practically indistinguishable. Journal: Applied Mathematical Finance Pages: 377-397 Issue: 5 Volume: 17 Year: 2010 Keywords: Credit default swap, reduced form model, Sato process, time-changed Levy process, cumulative hazard, X-DOI: 10.1080/13504860903357292 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903357292 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:5:p:377-397 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Løchte Jørgensen Author-X-Name-First: Peter Løchte Author-X-Name-Last: Jørgensen Author-Name: Domenico De Giovanni Author-X-Name-First: Domenico Author-X-Name-Last: De Giovanni Title: Time Charters with Purchase Options in Shipping: Valuation and Risk Management Abstract: The article studies the valuation and optimal management of Time Charters with Purchase Options (T/C-POPs), which is a specific type of asset lease with embedded options that is common in shipping markets. T/C-POPs are economically significant and sometimes account for more than half of the stock market value of listed shipping companies. The main source of risk in markets for maritime transportation is the freight rate, and we therefore specify a single-factor continuous time model for the dynamic evolution of freight rates that allows us to price a wide variety of freight rate-related derivatives including various forms of T/C-POPs using contingent claims valuation techniques. Our model allows for the derivation of closed valuation formulas for some simple freight rate derivatives, whereas the more complex ones are analysed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed. Journal: Applied Mathematical Finance Pages: 399-430 Issue: 5 Volume: 17 Year: 2010 Keywords: Ship valuation, options on ships, leasing, lease contracts with options, optimal stopping, X-DOI: 10.1080/13504860903388008 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903388008 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:5:p:399-430 Template-Type: ReDIF-Article 1.0 Author-Name: Ryosuke Ishii Author-X-Name-First: Ryosuke Author-X-Name-Last: Ishii Title: Optimal Execution in a Market with Small Investors Abstract: The author considers the dynamic trading strategies that minimize the expected cost of trading a large block of securities over a fixed finite number of periods. In this model, the market impact function that yields the execution prices for individual trades is endogeneously determined. This analysis is novel in that it introduces small investors, who do not affect the price flow, and a noise trader as market participants other than the institutional investors into a general equilibrium model. It is found that the institutional investor takes a rather complicated strategy to make use of its private information. As a result, the price impact not only changes over time but also depends on the trade history. Although there are several studies that deal with this topic in the recent empirical literature, it has remained unnoticed in the context of the theoretical optimal execution model. Journal: Applied Mathematical Finance Pages: 431-451 Issue: 5 Volume: 17 Year: 2010 Keywords: optimal execution, impact function, general equilibrium, X-DOI: 10.1080/13504860903415686 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903415686 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:5:p:431-451 Template-Type: ReDIF-Article 1.0 Author-Name: Reik Borger Author-X-Name-First: Reik Author-X-Name-Last: Borger Author-Name: Jan van Heys Author-X-Name-First: Jan Author-X-Name-Last: van Heys Title: Calibration of the Libor Market Model Using Correlations Implied by CMS Spread Options Abstract: This work discusses the calibration of instantaneous Libor correlations in the Libor market model. We extend the existing calibration strategies by the incorporation of spread option implied correlation information. The correlation structure implied by constant maturity swap (CMS) spread options observed in the present-day market motivates us to extend the existing parameterizations of ratio correlations by a new three-parameter approach. For the first time, this paper presents an extensive empirical study of different parameterizations and their capability to match market correlations. We can show that our approach leads to stable calibrations and gives a satisfactory fit to the market. We conclude our investigation with the pricing of a callable swap on CMS spread using the parameterizations compared before. Journal: Applied Mathematical Finance Pages: 453-469 Issue: 5 Volume: 17 Year: 2010 Keywords: LMM, calibration, correlation, market analysis, CMS spread option, X-DOI: 10.1080/13504860903541317 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903541317 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:5:p:453-469 Template-Type: ReDIF-Article 1.0 Author-Name: Alexander Schied Author-X-Name-First: Alexander Author-X-Name-Last: Schied Author-Name: Torsten Schoneborn Author-X-Name-First: Torsten Author-X-Name-Last: Schoneborn Author-Name: Michael Tehranchi Author-X-Name-First: Michael Author-X-Name-Last: Tehranchi Title: Optimal Basket Liquidation for CARA Investors is Deterministic Abstract: We consider the problem faced by an investor who must liquidate a given basket of assets over a finite time horizon. The investor's goal is to maximize the expected utility of the sales revenues over a class of adaptive strategies. We assume that the investor's utility has constant absolute risk aversion (CARA) and that the asset prices are given by a very general continuous-time, multiasset price impact model. Our main result is that (perhaps surprisingly) the investor does no worse if he narrows his search to deterministic strategies. In the case where the asset prices are given by an extension of the nonlinear price impact model of Almgren [(2003) Applied Mathematical Finance, 10, pp. 1-18], we characterize the unique optimal strategy via the solution of a Hamilton equation and the value function via a nonlinear partial differential equation with singular initial condition. Journal: Applied Mathematical Finance Pages: 471-489 Issue: 6 Volume: 17 Year: 2010 Keywords: Market impact modelling, illiquid markets, optimal liquidation, optimal trade execution, algorithmic trading, utility maximization, Hamilton-Jacobi-Bellman equation, finite fuel control, X-DOI: 10.1080/13504860903565050 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504860903565050 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:6:p:471-489 Template-Type: ReDIF-Article 1.0 Author-Name: Emmanuel Denis Author-X-Name-First: Emmanuel Author-X-Name-Last: Denis Title: Approximate Hedging of Contingent Claims under Transaction Costs for General Pay-offs Abstract: In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black-Scholes formula with a suitably enlarged volatility for a periodically revised portfolio whose terminal value approximates the pay-off h(S T) = (S T - K)+ of the call option. In subsequent studies, Lott, Kabanov and Safarian, and Gamys and Kabanov provided a rigorous mathematical analysis and established that the hedging portfolio approximates this pay-off in the case where the transaction costs decrease to zero as the number of revisions tends to infinity. The arguments used heavily the explicit expressions given by the Black-Scholes formula leaving open the problem whether the Leland approach holds for more general options and other types of price processes. In this paper we show that for a large class of the pay-off functions Leland's method can be successfully applied. On the other hand, if the pay-off function h(x) is not convex, then this method does not work. Journal: Applied Mathematical Finance Pages: 491-518 Issue: 6 Volume: 17 Year: 2010 Keywords: Black-Scholes formula, transaction costs, Leland's strategy, approximate hedging, X-DOI: 10.1080/13504861003590170 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003590170 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:6:p:491-518 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Monoyios Author-X-Name-First: Michael Author-X-Name-Last: Monoyios Title: Utility-Based Valuation and Hedging of Basis Risk With Partial Information Abstract: We analyse the valuation and hedging of a claim on a non-traded asset using a correlated traded asset under a partial information scenario, when the asset drifts are unknown constants. Using a Kalman filter and a Gaussian prior distribution for the unknown parameters, a full information model with random drifts is obtained. This is subjected to exponential indifference valuation. An expression for the optimal hedging strategy is derived. An asymptotic expansion for small values of risk aversion is obtained via partial differentiation equation (PDE) methods, following on from payoff decompositions and a price representation equation. Analytic and semi-analytic formulae for the terms in the expansion are obtained when the minimal entropy measure coincides with the minimal martingale measure. Simulation experiments are carried out which indicate that the filtering procedure can be beneficial in hedging, but sometimes needs to be augmented with the increased option premium, which takes into account parameter uncertainty in order to be effective. Empirical examples are presented which conform to these conclusions. Journal: Applied Mathematical Finance Pages: 519-551 Issue: 6 Volume: 17 Year: 2010 Keywords: Indifference valuation, partial information, basis risk, filtering, X-DOI: 10.1080/13504861003650883 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003650883 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:17:y:2010:i:6:p:519-551 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Kallsen Author-X-Name-First: Jan Author-X-Name-Last: Kallsen Author-Name: Arnd Pauwels Author-X-Name-First: Arnd Author-X-Name-Last: Pauwels Title: Variance-Optimal Hedging for Time-Changed Levy Processes Abstract: In this article, we solve the variance-optimal hedging problem in stochastic volatility (SV) models based on time-changed Levy processes, that is, in the setup of Carr et al. (2003). The solution is derived using results for general affine models in the companion article [Kallsen and Pauwels (2009)]. Journal: Applied Mathematical Finance Pages: 1-28 Issue: 1 Volume: 18 Year: 2011 Keywords: Variance-optimal hedging, Stochastic volatility, Time-changed Levy process, Laplace transform, X-DOI: 10.1080/13504861003669164 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003669164 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:1:p:1-28 Template-Type: ReDIF-Article 1.0 Author-Name: Ping Chen Author-X-Name-First: Ping Author-X-Name-Last: Chen Author-Name: Hailiang Yang Author-X-Name-First: Hailiang Author-X-Name-Last: Yang Title: Markowitz's Mean-Variance Asset-Liability Management with Regime Switching: A Multi-Period Model Abstract: This paper considers an optimal portfolio selection problem under Markowitz's mean-variance portfolio selection problem in a multi-period regime-switching model. We assume that there are n + 1 securities in the market. Given an economic state which is modelled by a finite state Markov chain, the return of each security at a fixed time point is a random variable. The return random variables may be different if the economic state is changed even for the same security at the same time point. We start our analysis from the no-liability case, in the spirit of Li and Ng (2000), both the optimal investment strategy and the efficient frontier are derived. Then we add uncontrollable liability into the model. By direct comparison with the no-liability case, the optimal strategy can be derived explicitly. Journal: Applied Mathematical Finance Pages: 29-50 Issue: 1 Volume: 18 Year: 2011 Keywords: discrete time, multi-period, regime switching, markov chain, asset-liability management, portfolio selection, efficient frontier, X-DOI: 10.1080/13504861003703633 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003703633 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:1:p:29-50 Template-Type: ReDIF-Article 1.0 Author-Name: Joanna Goard Author-X-Name-First: Joanna Author-X-Name-Last: Goard Title: A Time-Dependent Variance Model for Pricing Variance and Volatility Swaps Abstract: Analytic solutions are found for prices of variance and volatility swaps under a new time-dependent stochastic model for the dynamics of variance. The main features of the new stochastic differential equation are (1) an empirically validated cν3/2 diffusion term and (2) a free function of time as a moving target in a reversion term, allowing additional flexibility for model calibration against market data. Journal: Applied Mathematical Finance Pages: 51-70 Issue: 1 Volume: 18 Year: 2011 Keywords: variance swap, volatility swap, stochastic variance, X-DOI: 10.1080/13504861003795019 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003795019 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:1:p:51-70 Template-Type: ReDIF-Article 1.0 Author-Name: Gunther Leobacher Author-X-Name-First: Gunther Author-X-Name-Last: Leobacher Author-Name: Philip Ngare Author-X-Name-First: Philip Author-X-Name-Last: Ngare Title: On Modelling and Pricing Rainfall Derivatives with Seasonality Abstract: We are interested in pricing rainfall options written on precipitation at specific locations. We assume the existence of a tradeable financial instrument in the market whose price process is affected by the quantity of rainfall. We then construct a suitable 'Markovian gamma' model for the rainfall process which accounts for the seasonal change of precipitation and show how maximum likelihood estimators can be obtained for its parameters. We derive optimal strategies for exponential utility from terminal wealth and determine the utility indifference price of the claim. The method is illustrated with actual measured data on rainfall from a location in Kenya and spot prices of Kenyan electricity companies. Journal: Applied Mathematical Finance Pages: 71-91 Issue: 1 Volume: 18 Year: 2011 Keywords: Rainfall derivatives, Seasonality, Discrete-time Markov control process, Utility indifference pricing, Monte Carlo methods, X-DOI: 10.1080/13504861003795167 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003795167 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:1:p:71-91 Template-Type: ReDIF-Article 1.0 Author-Name: Andrea Barth Author-X-Name-First: Andrea Author-X-Name-Last: Barth Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Author-Name: Jurgen Potthoff Author-X-Name-First: Jurgen Author-X-Name-Last: Potthoff Title: Hedging of Spatial Temperature Risk with Market-Traded Futures Abstract: The main objective of this work is to construct optimal temperature futures from available market-traded contracts to hedge spatial risk. Temperature dynamics are modelled by a stochastic differential equation with spatial dependence. Optimal positions in market-traded futures minimizing the variance are calculated. Examples with numerical simulations based on a fast algorithm for the generation of random fields are presented. Journal: Applied Mathematical Finance Pages: 93-117 Issue: 2 Volume: 18 Year: 2011 Keywords: Temperature futures, Hedging, Spatio-temporal random fields, Heating and cooling degree-days, Stochastic simulation, X-DOI: 10.1080/13504861003722385 File-URL: http://www.tandfonline.com/doi/abs/10.1080/13504861003722385 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:2:p:93-117 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Pierre Fouque Author-X-Name-First: Jean-Pierre Author-X-Name-Last: Fouque Author-Name: Eli Kollman Author-X-Name-First: Eli Author-X-Name-Last: Kollman Title: Calibration of Stock Betas from Skews of Implied Volatilities Abstract: We develop call option price approximations for both the market index and an individual asset using a singular perturbation of a continuous-time capital asset pricing model in a stochastic volatility environment. These approximations show the role played by the asset's beta parameter as a component of the parameters of the call option price of the asset. They also show how these parameters, in combination with the parameters of the call option price for the market, can be used to extract the beta parameter. Finally, a calibration technique for the beta parameter is derived using the estimated option price parameters of both the asset and market index. The resulting estimator of the beta parameter is not only simple to implement but has the advantage of being forward looking as it is calibrated from skews of implied volatilities. Journal: Applied Mathematical Finance Pages: 119-137 Issue: 2 Volume: 18 Year: 2011 Keywords: CAPM, stock betas, stochastic volatility, implied volatilities, X-DOI: 10.1080/1350486X.2010.481175 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.481175 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:2:p:119-137 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Kwiatkowski Author-X-Name-First: Jan Author-X-Name-Last: Kwiatkowski Author-Name: Riccardo Rebonato Author-X-Name-First: Riccardo Author-X-Name-Last: Rebonato Title: A Coherent Aggregation Framework for Stress Testing and Scenario Analysis Abstract: We present a methodology to aggregate in a coherent manner conditional stress losses in a trading or banking book. The approach bypasses the specification of unconditional probabilities of the individual stress events and ensures by a linear programming approach so that the (subjective or frequentist) conditional probabilities chosen by the risk manager are internally consistent. The admissibility requirement greatly reduces the degree of arbitrariness in the conditional probability matrix if this is assigned subjectively. The approach can be used to address the requirements of the regulators on the Instantaneous Risk Charge. Journal: Applied Mathematical Finance Pages: 139-154 Issue: 2 Volume: 18 Year: 2011 Keywords: Stress testing, linear programming, coherent probabilities, X-DOI: 10.1080/1350486X.2010.491966 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.491966 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:2:p:139-154 Template-Type: ReDIF-Article 1.0 Author-Name: David German Author-X-Name-First: David Author-X-Name-Last: German Title: Corrections to the Prices of Derivatives due to Market Incompleteness Abstract: We compute the first-order corrections to marginal utility-based prices with respect to a 'small' number of random endowments in the framework of three incomplete financial models. They are a stochastic volatility model, a basis risk and market portfolio model and a credit-risk model with jumps and stochastic recovery rate. Journal: Applied Mathematical Finance Pages: 155-187 Issue: 2 Volume: 18 Year: 2011 Keywords: Price corrections, risk tolerance, stochastic volatility, basis risk, credit risk, X-DOI: 10.1080/1350486X.2010.493709 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.493709 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:2:p:155-187 Template-Type: ReDIF-Article 1.0 Author-Name: Damien Challet Author-X-Name-First: Damien Author-X-Name-Last: Challet Title: The Tick-by-Tick Dynamical Consistency of Price Impact in Limit Order Books Abstract: Constant price impact functions, much used in financial literature, are shown to give rise to paradoxical outcomes as they do not allow for proper predictability removal: for instance, the exploitation of a single large trade whose size and time of execution are known in advance to some insider leaves the arbitrage opportunity unchanged, which allows arbitrage exploitation multiple times. We argue that chain arbitrage exploitation should not exist, which provides an a contrario consistency criterion. Remarkably, all the stocks investigated in the Paris Stock Exchange have dynamically consistent price impact functions. Both the bid-ask spread and the feedback of sequential same-side market orders onto both sides of the order book are essential to ensure consistency at the smallest time scale. Journal: Applied Mathematical Finance Pages: 189-205 Issue: 3 Volume: 18 Year: 2011 Keywords: Limit order markets, efficiency, market impact, consistency condition, arbitrage, X-DOI: 10.1080/1350486X.2010.504333 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.504333 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:3:p:189-205 Template-Type: ReDIF-Article 1.0 Author-Name: Louis Paulot Author-X-Name-First: Louis Author-X-Name-Last: Paulot Author-Name: Xavier Lacroze Author-X-Name-First: Xavier Author-X-Name-Last: Lacroze Title: One-Dimensional Pricing of CPPI Abstract: Constant Proportion Portfolio Insurance (CPPI) is an investment strategy designed to give participation in the performance of a risky asset while protecting the invested capital. This protection is, however, not perfect and the gap risk must be quantified. CPPI strategies are path dependent and may have American exercise which makes their valuation complex. A naive description of the state of the portfolio would involve three or even four variables. In this article we prove that the system can be described as a discrete-time Markov process in one single variable if the underlying asset follows a process with independent increments. This yields an efficient pricing scheme using transition probabilities. Our framework is flexible enough to handle most features of traded CPPIs including profit lock-in and other kinds of strategies with discrete-time reallocation. Journal: Applied Mathematical Finance Pages: 207-225 Issue: 3 Volume: 18 Year: 2011 Keywords: CPPI, portfolio insurance, option, pricing, gap risk, markov, X-DOI: 10.1080/1350486X.2010.486571 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.486571 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:3:p:207-225 Template-Type: ReDIF-Article 1.0 Author-Name: Dilip Madan Author-X-Name-First: Dilip Author-X-Name-Last: Madan Author-Name: Marc Yor Author-X-Name-First: Marc Author-X-Name-Last: Yor Title: The S&P 500 Index as a Sato Process Travelling at the Speed of the VIX Abstract: The logarithm of the S&P 500 Index is modelled as a Sato process running at a speed proportional to the current level of the VIX. When the VIX is itself modelled as the exponential of a compound Poisson process with drift, we show that exact expressions are available for the prices of equity options, taken at an independent exponential maturity. The parameters for the compound Poisson process are calibrated from VIX options whereas the parameters for the Sato process driving the stock may be inferred from market option prices. Results confirm that both the S&P 500 index option surface and the parameters of the VIX time-changed Sato process have volatilities, skews and term volatility spreads that are responsive to the VIX level and the VIX option surface. Journal: Applied Mathematical Finance Pages: 227-244 Issue: 3 Volume: 18 Year: 2011 Keywords: Quadratic variation options, VGSSD process, independent beta variates, X-DOI: 10.1080/1350486X.2010.486558 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.486558 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:3:p:227-244 Template-Type: ReDIF-Article 1.0 Author-Name: Gerald Cheang Author-X-Name-First: Gerald Author-X-Name-Last: Cheang Author-Name: Carl Chiarella Author-X-Name-First: Carl Author-X-Name-Last: Chiarella Title: Exchange Options Under Jump-Diffusion Dynamics Abstract: This article extends the exchange option model of Margrabe, where the distributions of both stock prices are log-normal with correlated Wiener components, to allow the underlying assets to be driven by jump-diffusion processes of the type originally introduced by Merton. We introduce the Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the Radon-Nikodym derivative allows us to price the option under different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic interpretation of the early exercise premium. Journal: Applied Mathematical Finance Pages: 245-276 Issue: 3 Volume: 18 Year: 2011 Keywords: American options, exchange options, compound Poisson processes, equivalent martingale measure, X-DOI: 10.1080/1350486X.2010.505390 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.505390 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:3:p:245-276 Template-Type: ReDIF-Article 1.0 Author-Name: Ghulam Sorwar Author-X-Name-First: Ghulam Author-X-Name-Last: Sorwar Author-Name: Giovanni Barone-Adesi Author-X-Name-First: Giovanni Author-X-Name-Last: Barone-Adesi Title: Valuation of Two-Factor Interest Rate Contingent Claims Using Green's Theorem Abstract: Over the years a number of two-factor interest rate models have been proposed that have formed the basis for the valuation of interest rate contingent claims. This valuation equation often takes the form of a partial differential equation that is solved using the finite difference approach. In the case of two-factor models this has resulted in solving two second-order partial derivatives leading to boundary errors, as well as numerous first-order derivatives. In this article we demonstrate that using Green's theorem, second-order derivatives can be reduced to first-order derivatives that can be easily discretized; consequently, two-factor partial differential equations are easier to discretize than one-factor partial differential equations. We illustrate our approach by applying it to value contingent claims based on the two-factor CIR model. We provide numerical examples that illustrate that our approach shows excellent agreement with analytical prices and the popular Crank-Nicolson method. Journal: Applied Mathematical Finance Pages: 277-289 Issue: 4 Volume: 18 Year: 2011 Keywords: Box method, derivatives, Green's theorem, X-DOI: 10.1080/1350486X.2010.531588 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.531588 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:4:p:277-289 Template-Type: ReDIF-Article 1.0 Author-Name: Daniel Ostrov Author-X-Name-First: Daniel Author-X-Name-Last: Ostrov Author-Name: Thomas Wong Author-X-Name-First: Thomas Author-X-Name-Last: Wong Title: Optimal Asset Allocation for Passive Investing with Capital Loss Harvesting Abstract: This article examines how to quantify and optimally utilize the beneficial effect that capital loss harvesting generates in a taxable portfolio. We explicitly determine the optimal initial asset allocation for an investor who follows the continuous time dynamic trading strategy of Constantinides (1983). This strategy sells and re-buys all stocks with losses, but is otherwise passive. Our model allows the use of the stock position's full purchase history for computing the cost basis. The method can also be used to rebalance at later times. For portfolios with one stock position and cash, the probability density function for the portfolio's state corresponds to the solution of a 3-space + 1-time dimensional partial differential equation (PDE) with an oblique reflecting boundary condition. Extensions of this PDE, including to the case of multiple correlated stocks, are also presented. We detail a numerical algorithm for the PDE in the single stock case. The algorithm shows the significant effect capital loss harvesting can have on the optimal stock allocation, and it also allows us to compute the expected additional return that capital loss harvesting generates. Our PDE-based algorithm, compared with Monte Carlo methods, is shown to generate much more precise results in a fraction of the time. Finally, we employ Monte Carlo methods to approximate the impact of many of our model's assumptions. Journal: Applied Mathematical Finance Pages: 291-329 Issue: 4 Volume: 18 Year: 2011 Keywords: Taxes, capital losses, portfolio optimization, expected utility, passive investing, X-DOI: 10.1080/1350486X.2010.513499 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.513499 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:4:p:291-329 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Spreij Author-X-Name-First: Peter Author-X-Name-Last: Spreij Author-Name: Enno Veerman Author-X-Name-First: Enno Author-X-Name-Last: Veerman Author-Name: Peter Vlaar Author-X-Name-First: Peter Author-X-Name-Last: Vlaar Title: An Affine Two-Factor Heteroskedastic Macro-Finance Term Structure Model Abstract: We propose an affine macro-finance term structure model for interest rates that allows for both constant volatilities (homoskedastic model) and state-dependent volatilities (heteroskedastic model). In a homoskedastic model, interest rates are symmetric, which means that either very low interest rates are predicted too often or very high interest rates not often enough. This undesirable symmetry for constant volatility models motivates the use of heteroskedastic models where the volatility depends on the driving factors. For a truly heteroskedastic model in continuous time, which involves a multivariate square root process, the so-called Feller conditions are usually imposed to ensure that the roots have non-negative arguments. For a discrete time approximate model, the Feller conditions do not give this guarantee. Moreover, in a macro-finance context, the restrictions imposed might be economically unappealing. It has also been observed that even without the Feller conditions imposed, for a practically relevant term structure model, negative arguments rarely occur. Using models estimated on German data, we compare the yields implied by (approximate) analytic exponentially affine expressions to those obtained through Monte Carlo simulations of very high numbers of sample paths. It turns out that the differences are rarely statistically significant, whether the Feller conditions are imposed or not. Moreover, economically, the differences are negligible, as they are always below one basis point. Journal: Applied Mathematical Finance Pages: 331-352 Issue: 4 Volume: 18 Year: 2011 Keywords: Macro-finance models, affine term structure model, expected inflation, ex ante real short rate, Monte Carlo simulations, X-DOI: 10.1080/1350486X.2010.517664 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.517664 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:4:p:331-352 Template-Type: ReDIF-Article 1.0 Author-Name: Dejun Xie Author-X-Name-First: Dejun Author-X-Name-Last: Xie Author-Name: David Edwards Author-X-Name-First: David Author-X-Name-Last: Edwards Author-Name: Gilberto Schleiniger Author-X-Name-First: Gilberto Author-X-Name-Last: Schleiniger Author-Name: Qinghua Zhu Author-X-Name-First: Qinghua Author-X-Name-Last: Zhu Title: Characterization of the American Put Option Using Convexity Abstract: Understanding the behaviour of the American put option is one of the classic problems in mathematical finance. Considerable efforts have been made to understand the asymptotic expansion of the optimal early exercise boundary for small time near expiry. Here we focus on the large-time expansion of the boundary. Based on a recent development of the convexity property, we are able to establish two integral identities pertaining to the boundary, from which the upper bound of its large-time expansion is derived. The bound includes parameter dependence in the exponential decay to its limiting value. In addition, these time explicit identities provide very efficient numerical approximations to the true solution to the problem. Journal: Applied Mathematical Finance Pages: 353-365 Issue: 4 Volume: 18 Year: 2011 Keywords: asymptotic analysis, free boundary-value problem, American put option, X-DOI: 10.1080/1350486X.2010.524359 File-URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.524359 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:4:p:353-365 Template-Type: ReDIF-Article 1.0 Author-Name: Tomáš Bokes Author-X-Name-First: Tomáš Author-X-Name-Last: Bokes Author-Name: Daniel Ševčovič Author-X-Name-First: Daniel Author-X-Name-Last: Ševčovič Title: Early Exercise Boundary for American Type of Floating Strike Asian Option and Its Numerical Approximation Abstract: In this article, we generalize and analyse the model for pricing American-style Asian options proposed by Hansen and Jørgensen (2000) by including a continuous dividend rate q and a general method of averaging the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The first-order expansion in terms of of the early exercise boundary close to expiry is constructed. We furthermore propose an efficient numerical algorithm for determining the early exercise boundary position based on the front-fixing method. Construction of the algorithm is based on a solution to a non-local parabolic partial differential equation for the transformed variable representing the synthesized portfolio. Various numerical results and comparisons of our numerical method and the method developed by Dai and Kwok (2006) are presented. Journal: Applied Mathematical Finance Pages: 367-394 Issue: 5 Volume: 18 Year: 2010 Month: 11 X-DOI: 10.1080/1350486X.2010.547041 File-URL: http://hdl.handle.net/10.1080/1350486X.2010.547041 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:5:p:367-394 Template-Type: ReDIF-Article 1.0 Author-Name: Julian Lorenz Author-X-Name-First: Julian Author-X-Name-Last: Lorenz Author-Name: Robert Almgren Author-X-Name-First: Robert Author-X-Name-Last: Almgren Title: Mean--Variance Optimal Adaptive Execution Abstract: Electronic trading of equities and other securities makes heavy use of ‘arrival price’ algorithms that balance the market impact cost of rapid execution against the volatility risk of slow execution. In the standard formulation, mean--variance optimal trading strategies are static: they do not modify the execution speed in response to price motions observed during trading. We show that substantial improvement is possible by using dynamic trading strategies and that the improvement is larger for large initial positions. We develop a technique for computing optimal dynamic strategies to any desired degree of precision. The asset price process is observed on a discrete tree with an arbitrary number of levels. We introduce a novel dynamic programming technique in which the control variables are not only the shares traded at each time step but also the maximum expected cost for the remainder of the program; the value function is the variance of the remaining program. The resulting adaptive strategies are ‘aggressive-in-the-money’: they accelerate the execution when the price moves in the trader's favor, spending parts of the trading gains to reduce risk. Journal: Applied Mathematical Finance Pages: 395-422 Issue: 5 Volume: 18 Year: 2011 Month: 1 X-DOI: 10.1080/1350486X.2011.560707 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.560707 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:5:p:395-422 Template-Type: ReDIF-Article 1.0 Author-Name: Nairn McWilliams Author-X-Name-First: Nairn Author-X-Name-Last: McWilliams Author-Name: Sotirios Sabanis Author-X-Name-First: Sotirios Author-X-Name-Last: Sabanis Title: Arithmetic Asian Options under Stochastic Delay Models Abstract: Motivated by the increasing interest in past-dependent asset pricing models, shown in recent years by market practitioners and prominent authors such as Hobson and Rogers (1998, Complete models with stochastic volatility, Mathematical Finance, 8(1), pp. 27--48), we explore option pricing techniques for arithmetic Asian options under a stochastic delay differential equation approach. We obtain explicit closed-form expressions for a number of lower and upper bounds and compare their accuracy numerically. Journal: Applied Mathematical Finance Pages: 423-446 Issue: 5 Volume: 18 Year: 2011 Month: 2 X-DOI: 10.1080/1350486X.2011.567119 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.567119 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:5:p:423-446 Template-Type: ReDIF-Article 1.0 Author-Name: Aanand Venkatramanan Author-X-Name-First: Aanand Author-X-Name-Last: Venkatramanan Author-Name: Carol Alexander Author-X-Name-First: Carol Author-X-Name-Last: Alexander Title: Closed Form Approximations for Spread Options Abstract: This article expresses the price of a spread option as the sum of the prices of two compound options. One compound option is to exchange vanilla call options on the two underlying assets and the other is to exchange the corresponding put options. This way we derive a new closed form approximation for the price of a European spread option and a corresponding approximation for each of its price, volatility and correlation hedge ratios. Our approach has many advantages over existing analytical approximations, which have limited validity and an indeterminacy that renders them of little practical use. The compound exchange option approximation for European spread options is then extended to American spread options on assets that pay dividends or incur costs. Simulations quantify the accuracy of our approach; we also present an empirical application to the American crack spread options that are traded on NYMEX. For illustration, we compare our results with those obtained using the approximation attributed to Kirk (1996, Correlation in energy markets. In: V. Kaminski (Ed.), Managing Energy Price Risk, pp. 71--78 (London: Risk Publications)), which is commonly used by traders. Journal: Applied Mathematical Finance Pages: 447-472 Issue: 5 Volume: 18 Year: 2011 Month: 1 X-DOI: 10.1080/1350486X.2011.567120 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.567120 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:5:p:447-472 Template-Type: ReDIF-Article 1.0 Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Author-Name: Eric S. Fung Author-X-Name-First: Eric S. Author-X-Name-Last: Fung Author-Name: Michael K. Ng Author-X-Name-First: Michael K. Author-X-Name-Last: Ng Title: Option Valuation with a Discrete-Time Double Markovian Regime-Switching Model Abstract: This article develops an option valuation model in the context of a discrete-time double Markovian regime-switching (DMRS) model with innovations having a generic distribution. The DMRS model is more flexible than the traditional Markovian regime-switching model in the sense that the drift and the volatility of the price dynamics of the underlying risky asset are modulated by two observable, discrete-time and finite-state Markov chains, so that they are not perfectly correlated. The states of each of the chains represent states of proxies of (macro)economic factors. Here we consider the situation that one (macro)economic factor is caused by the other (macro)economic factor. The market model is incomplete, and so there is more than one equivalent martingale measure. We employ a discrete-time version of the regime-switching Esscher transform to determine an equivalent martingale measure for valuation. Different parametric distributions for the innovations of the price dynamics of the underlying risky asset are considered. Simulation experiments are conducted to illustrate the implementation of the model and to document the impacts of the macroeconomic factors described by the chains on the option prices under various different parametric models for the innovations. Journal: Applied Mathematical Finance Pages: 473-490 Issue: 6 Volume: 18 Year: 2011 Month: 3 X-DOI: 10.1080/1350486X.2011.578457 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.578457 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:6:p:473-490 Template-Type: ReDIF-Article 1.0 Author-Name: Catherine Donnelly Author-X-Name-First: Catherine Author-X-Name-Last: Donnelly Title: Good-Deal Bounds in a Regime-Switching Diffusion Market Abstract: We consider option pricing in a regime-switching diffusion market. As the market is incomplete, there is no unique price for a derivative. We apply the good-deal pricing bounds idea to obtain ranges for the price of a derivative. As an illustration, we calculate the good-deal pricing bounds for a European call option and we also examine the stability of these bounds when we change the generator of the Markov chain which drives the regime-switching. We find that the pricing bounds depend strongly on the choice of the generator. Journal: Applied Mathematical Finance Pages: 491-515 Issue: 6 Volume: 18 Year: 2011 Month: 5 X-DOI: 10.1080/1350486X.2011.591156 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.591156 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:6:p:491-515 Template-Type: ReDIF-Article 1.0 Author-Name: Martin Forde Author-X-Name-First: Martin Author-X-Name-Last: Forde Author-Name: Antoine Jacquier Author-X-Name-First: Antoine Author-X-Name-Last: Jacquier Title: Small-Time Asymptotics for an Uncorrelated Local-Stochastic Volatility Model Abstract: We add some rigour to the work of Henry-Labordère (2009; Analysis, Geometry, and Modeling in Finance: Advanced Methods in Option Pricing (London and New York: Chapman & Hall)), Lewis (2007; Geometries and Smile Asymptotics for a Class of Stochastic Volatility Models. Available at http://www.optioncity.net (accessed 28 May 2011)) and Paulot (2009; Asymptotic implied volatility at the second order with application to the SABR model, Working Paper, Available at papers.ssrn.com/sol3/papers.cfm?abstract_id=1413649 (accessed 11 June 2011)) on the small-time behaviour of a local-stochastic volatility model with zero correlation at leading order. We do this using the Freidlin—Wentzell (FW) theory of large deviations for stochastic differential equations (SDEs), and then converting to a differential geometry problem of computing the shortest geodesic from a point to a vertical line on a Riemmanian manifold, whose metric is induced by the inverse of the diffusion coefficient. The solution to this variable endpoint problem is obtained using a transversality condition, where the geodesic is perpendicular to the vertical line under the aforementioned metric. We then establish the corresponding small-time asymptotic behaviour for call options using Hölder's inequality, and the implied volatility (using a general result in Roper and Rutkowski (forthcoming, A note on the behavior of the Black--Scholes implied volatility close to expiry, International Journal of Thoretical and Applied Finance). We also derive a series expansion for the implied volatility in the small-maturity limit, in powers of the log-moneyness, and we show how to calibrate such a model to the observed implied volatility smile in the small-maturity limit. Journal: Applied Mathematical Finance Pages: 517-535 Issue: 6 Volume: 18 Year: 2011 Month: 4 X-DOI: 10.1080/1350486X.2011.591159 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.591159 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:6:p:517-535 Template-Type: ReDIF-Article 1.0 Author-Name: Goran Peskir Author-X-Name-First: Goran Author-X-Name-Last: Peskir Author-Name: Farman Samee Author-X-Name-First: Farman Author-X-Name-Last: Samee Title: The British Put Option Abstract: We present a new put option where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature which is key to the British put option. Should the option holder believe the true drift of the stock price to be unfavourable (based upon the observed price movements) he can substitute the true drift with the contract drift and minimize his losses. The practical implications of this protection feature are most remarkable as not only can the option holder exercise at or above the strike price to a substantial reimbursement of the original option price (covering the ability to sell in a liquid option market completely endogenously) but also when the stock price movements are favourable he will generally receive higher returns at a lesser price. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results we perform a financial analysis of the British put option that leads to the conclusions above and shows that with the contract drift properly selected the British put option becomes a very attractive alternative to the classic American put. Journal: Applied Mathematical Finance Pages: 537-563 Issue: 6 Volume: 18 Year: 2011 Month: 4 X-DOI: 10.1080/1350486X.2011.591167 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.591167 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:18:y:2011:i:6:p:537-563 Template-Type: ReDIF-Article 1.0 Author-Name: Lech A. Grzelak Author-X-Name-First: Lech A. Author-X-Name-Last: Grzelak Author-Name: Cornelis W. Oosterlee Author-X-Name-First: Cornelis W. Author-X-Name-Last: Oosterlee Title: On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates Abstract: We construct multi-currency models with stochastic volatility (SV) and correlated stochastic interest rates with a full matrix of correlations. We first deal with a foreign exchange (FX) model of Heston-type, in which the domestic and foreign interest rates are generated by the short-rate process of Hull--White (Hull, J. and White, A. [1990] Pricing interest-rate derivative securities, Review of Financial Studies, 3, pp. 573--592). We then extend the framework by modelling the interest rate by an SV displaced-diffusion (DD) Libor Market Model (Andersen, L. B. G. and Andreasen, J. [2000] Volatility skews and extensions of the libor market model, Applied Mathematics Finance, 1[7], pp. 1--32), which can model an interest rate smile. We provide semi-closed form approximations which lead to efficient calibration of the multi-currency models. Finally, we add a correlated stock to the framework and discuss the construction, model calibration and pricing of equity--FX--interest rate hybrid pay-offs. Journal: Applied Mathematical Finance Pages: 1-35 Issue: 1 Volume: 19 Year: 2012 Month: 2 X-DOI: 10.1080/1350486X.2011.570492 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.570492 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:1:p:1-35 Template-Type: ReDIF-Article 1.0 Author-Name: Alexander Buryak Author-X-Name-First: Alexander Author-X-Name-Last: Buryak Author-Name: Ivan Guo Author-X-Name-First: Ivan Author-X-Name-Last: Guo Title: New Analytic Approach to Address Put--Call Parity Violation due to Discrete Dividends Abstract: The issue of developing simple Black--Scholes (BS)-type approximations for pricing European options with large discrete dividends was popular since the early 2000s with a few different approaches reported during the last 10 years. Moreover, it has been claimed that at least some of the resulting expressions represent high-quality approximations which closely match the results obtained by the use of numerics. In this article we review, on the one hand, these previously suggested BS-type approximations and, on the other hand, different versions of the corresponding Crank--Nicolson (CN) numerical schemes with a primary focus on their boundary condition variations. Unexpectedly we often observe substantial deviations between the analytical and numerical results which may be especially pronounced for European puts. Moreover, our analysis demonstrates that any BS-type approximation which adjusts put parameters identically to call parameters has an inherent problem of failing to detect a little known put--call parity violation phenomenon. To address this issue, we derive a new analytic pricing approximation which is in better agreement with the corresponding numerical results in comparison with any of the previously known analytic approaches for European calls and puts with large discrete dividends. Journal: Applied Mathematical Finance Pages: 37-58 Issue: 1 Volume: 19 Year: 2012 Month: 5 X-DOI: 10.1080/1350486X.2011.591163 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.591163 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:1:p:37-58 Template-Type: ReDIF-Article 1.0 Author-Name: Wolfgang Karl Härdle Author-X-Name-First: Wolfgang Karl Author-X-Name-Last: Härdle Author-Name: Brenda López Cabrera Author-X-Name-First: Brenda López Author-X-Name-Last: Cabrera Title: The Implied Market Price of Weather Risk Abstract: Weather derivatives (WD) are end-products of a process known as securitization that transforms non-tradable risk factors (weather) into tradable financial assets. For pricing and hedging non-tradable assets, one essentially needs to incorporate the market price of risk (MPR), which is an important parameter of the associated equivalent martingale measure (EMM). The majority of papers so far has priced non-tradable assets assuming zero or constant MPR, but this assumption yields biased prices and has never been quantified earlier under the EMM framework. Given that liquid-derivative contracts based on daily temperature are traded on the Chicago Mercantile Exchange (CME), we infer the MPR from traded futures-type contracts (CAT, CDD, HDD and AAT). The results show how the MPR significantly differs from 0, how it varies in time and changes in sign. It can be parameterized, given its dependencies on time and temperature seasonal variation. We establish connections between the market risk premium (RP) and the MPR. Journal: Applied Mathematical Finance Pages: 59-95 Issue: 1 Volume: 19 Year: 2012 Month: 2 X-DOI: 10.1080/1350486X.2011.591170 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.591170 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:1:p:59-95 Template-Type: ReDIF-Article 1.0 Author-Name: C. Atkinson Author-X-Name-First: C. Author-X-Name-Last: Atkinson Author-Name: P. Ingpochai Author-X-Name-First: P. Author-X-Name-Last: Ingpochai Title: The Effect of Correlation and Transaction Costs on the Pricing of Basket Options Abstract: In this article, we examine the problem of evaluating the option price of a European call option written on N underlying assets when there are proportional transaction costs in the market. Since the portfolio under consideration consists of multiple risky assets, which makes numerical methods formidable, we use perturbation analyses. The article extends the model for option pricing on uncorrelated assets, which was proposed by Atkinson and Alexandropoulos (2006; Pricing a European basket option in the presence of proportional transaction cost, Applied Mathematical Finance, 13(3), pp. 191--214). We determine optimal hedging strategies as well as option prices on both correlated and uncorrelated assets. The option valuation problem is obtained by comparing the maximized utility of wealth with and without option liability. The two stochastic control problems, which arise from the transaction costs, are transformed to free boundary and partial differential equation problems. Once the problems have been formulated, we establish optimal trading strategies for each of the portfolios. In addition, the optimal hedging strategies can be found by comparing the trading strategies of the two portfolios. We provide a general procedure for solving N risky assets, which shows that for ‘small’ correlations the N asset problem can be replaced by N (N − 1)/2 two-dimensional problems and give numerical examples for the two risky assets portfolios. Journal: Applied Mathematical Finance Pages: 131-179 Issue: 2 Volume: 19 Year: 2012 Month: 6 X-DOI: 10.1080/1350486X.2011.601919 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.601919 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:2:p:131-179 Template-Type: ReDIF-Article 1.0 Author-Name: Erik Ekström Author-X-Name-First: Erik Author-X-Name-Last: Ekström Author-Name: Johan Tysk Author-X-Name-First: Johan Author-X-Name-Last: Tysk Title: Comparison of Two Methods for Superreplication Abstract: We compare two methods for superreplication of options with convex pay-off functions. One method entails the overestimation of an unknown covariance matrix in the sense of quadratic forms. With this method the value of the superreplicating portfolio is given as the solution of a linear Black--Scholes BS-type equation. In the second method, the choice of quadratic form is made pointwise. This leads to a fully non-linear equation, the so-called Black--Scholes--Barenblatt (BSB) equation, for the value of the superreplicating portfolio. In general, this value is smaller for the second method than for the first method. We derive estimates for the difference between the initial values of the superreplicating strategies obtained using the two methods. Journal: Applied Mathematical Finance Pages: 181-193 Issue: 2 Volume: 19 Year: 2012 Month: 8 X-DOI: 10.1080/1350486X.2011.616103 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.616103 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:2:p:181-193 Template-Type: ReDIF-Article 1.0 Author-Name: Hansjörg Albrecher Author-X-Name-First: Hansjörg Author-X-Name-Last: Albrecher Author-Name: Dominik Kortschak Author-X-Name-First: Dominik Author-X-Name-Last: Kortschak Author-Name: Xiaowen Zhou Author-X-Name-First: Xiaowen Author-X-Name-Last: Zhou Title: Pricing of Parisian Options for a Jump-Diffusion Model with Two-Sided Jumps Abstract: Using the solution of one-sided exit problem, a procedure to price Parisian barrier options in a jump-diffusion model with two-sided exponential jumps is developed. By extending the method developed in Chesney, Jeanblanc-Picqu� and Yor (1997; Brownian excursions and Parisian barrier options, Advances in Applied Probability, 29(1), pp. 165--184) for the diffusion case to the more general set-up, we arrive at a numerical pricing algorithm that significantly outperforms Monte Carlo simulation for the prices of such products. Journal: Applied Mathematical Finance Pages: 97-129 Issue: 2 Volume: 19 Year: 2012 Month: 7 X-DOI: 10.1080/1350486X.2011.599976 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.599976 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:2:p:97-129 Template-Type: ReDIF-Article 1.0 Author-Name: Kin Hung (Felix) Kan Author-X-Name-First: Kin Hung (Felix) Author-X-Name-Last: Kan Author-Name: R. Mark Reesor Author-X-Name-First: R. Mark Author-X-Name-Last: Reesor Title: Bias Reduction for Pricing American Options by Least-Squares Monte Carlo Abstract: We derive an approximation to the bias in regression-based Monte Carlo estimators of American option values. This derivation holds for general asset-price processes of any dimensionality and for general pay-off structures. It uses the large sample properties of least-squares regression estimators. Bias-corrected estimators result by subtracting the bias approximation from the uncorrected estimator at each exercise opportunity. Numerical results show that the bias-corrected estimator outperforms its uncorrected counterpart across all combinations of number of exercise opportunities, option moneyness and sample size. Finally, the results suggest significant computational efficiency increases can be realized through trivial parallel implementations using the corrected estimator. Journal: Applied Mathematical Finance Pages: 195-217 Issue: 3 Volume: 19 Year: 2012 Month: 7 X-DOI: 10.1080/1350486X.2011.608566 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.608566 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:195-217 Template-Type: ReDIF-Article 1.0 Author-Name: Robert J. Elliott Author-X-Name-First: Robert J. Author-X-Name-Last: Elliott Author-Name: John W. Lau Author-X-Name-First: John W. Author-X-Name-Last: Lau Author-Name: Hong Miao Author-X-Name-First: Hong Author-X-Name-Last: Miao Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Author-X-Name-Last: Kuen Siu Title: Viterbi-Based Estimation for Markov Switching GARCH Model Abstract: We outline a two-stage estimation method for a Markov-switching Generalized Autoregressive Conditional Heteroscedastic (GARCH) model modulated by a hidden Markov chain. The first stage involves the estimation of a hidden Markov chain using the Vitberi algorithm given the model parameters. The second stage uses the maximum likelihood method to estimate the model parameters given the estimated hidden Markov chain. Applications to financial risk management are discussed through simulated data. Journal: Applied Mathematical Finance Pages: 219-231 Issue: 3 Volume: 19 Year: 2012 Month: 8 X-DOI: 10.1080/1350486X.2011.620396 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.620396 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:219-231 Template-Type: ReDIF-Article 1.0 Author-Name: Pierre Étor� Author-X-Name-First: Pierre Author-X-Name-Last: Étor� Author-Name: Emmanuel Gobet Author-X-Name-First: Emmanuel Author-X-Name-Last: Gobet Title: Stochastic Expansion for the Pricing of Call Options with Discrete Dividends Abstract: In the context of an asset paying affine-type discrete dividends, we present closed analytical approximations for the pricing of European vanilla options in the Black--Scholes model with time-dependent parameters. They are obtained using a stochastic Taylor expansion around a shifted lognormal proxy model. The final formulae are, respectively, first-, second- and third- order approximations w.r.t. the fixed part of the dividends. Using Cameron--Martin transformations, we provide explicit representations of the correction terms as Greeks in the Black--Scholes model. The use of Malliavin calculus enables us to provide tight error estimates for our approximations. Numerical experiments show that this approach yields very accurate results, in particular compared with known approximations of Bos, Gairat and Shepeleva (2003, Dealing with discrete dividends, Risk Magazine, 16, pp. 109--112) and Veiga and Wystup (2009, Closed formula for option with discrete dividends and its derivatives, Applied Mathematical Finance, 16(6), pp. 517--531), and quicker than the iterated integration procedure of Haug, Haug and Lewis (2003, Back to basics: a new approach to the discrete dividend problem, Wilmott Magazine, pp. 37--47) or than the binomial tree method of Vellekoop and Nieuwenhuis (2006, Efficient pricing of derivatives on assets with discrete dividends, Applied Mathematical Finance, 13(3), pp. 265--284). Journal: Applied Mathematical Finance Pages: 233-264 Issue: 3 Volume: 19 Year: 2012 Month: 8 X-DOI: 10.1080/1350486X.2011.620397 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.620397 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:233-264 Template-Type: ReDIF-Article 1.0 Author-Name: Colin Atkinson Author-X-Name-First: Colin Author-X-Name-Last: Atkinson Author-Name: Gary Quek Author-X-Name-First: Gary Author-X-Name-Last: Quek Title: Dynamic Portfolio Optimization in Discrete-Time with Transaction Costs Abstract: A discrete-time model of portfolio optimization is studied under the effects of proportional transaction costs. A general class of underlying probability distributions is assumed for the returns of the asset prices. An investor with an exponential utility function seeks to maximize the utility of terminal wealth by determining the optimal investment strategy at the start of each time step. Dynamic programming is used to derive an algorithm for computing the optimal value function and optimal boundaries of the no-transaction region at each time step. In the limit of small transaction costs, perturbation analysis is applied to obtain the optimal value function and optimal boundaries at any time step in the rebalancing of the portfolio. Journal: Applied Mathematical Finance Pages: 265-298 Issue: 3 Volume: 19 Year: 2012 Month: 8 X-DOI: 10.1080/1350486X.2011.620775 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.620775 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:3:p:265-298 Template-Type: ReDIF-Article 1.0 Author-Name: Henryk Gzyl Author-X-Name-First: Henryk Author-X-Name-Last: Gzyl Author-Name: Silvia Mayoral Author-X-Name-First: Silvia Author-X-Name-Last: Mayoral Title: Determination of the Probability Distribution Measures from Market Option Prices Using the Method of Maximum Entropy in the Mean Abstract: We consider the problem of recovering the risk-neutral probability distribution of the price of an asset, when the information available consists of the market price of derivatives of European type having the asset as underlying. The information available may or may not include the spot value of the asset as data. When we only know the true empirical law of the underlying, our method will provide a measure that is absolutely continuous with respect to the empirical law, thus making our procedure model independent. If we assume that the prices of the derivatives include risk premia and/or transaction prices, using this method it is possible to estimate those values, as well as the no-arbitrage prices. This is of interest not only when the market is not complete, but also if for some reason we do not have information about the model for the price of the underlying. Journal: Applied Mathematical Finance Pages: 299-312 Issue: 4 Volume: 19 Year: 2012 Month: 8 X-DOI: 10.1080/1350486X.2011.621354 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.621354 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:4:p:299-312 Template-Type: ReDIF-Article 1.0 Author-Name: Stephen Chin Author-X-Name-First: Stephen Author-X-Name-Last: Chin Author-Name: Daniel Dufresne Author-X-Name-First: Daniel Author-X-Name-Last: Dufresne Title: A General Formula for Option Prices in a Stochastic Volatility Model Abstract: We consider the pricing of European derivatives in a Black--Scholes model with stochastic volatility. We show how Parseval's theorem may be used to express those prices as Fourier integrals. This is a significant improvement over Monte Carlo simulation. The main ingredient in our method is the Laplace transform of the ordinary (constant volatility) price of a put or call in the Black--Scholes model, where the transform is taken with respect to maturity (T); this does not appear to have been used before in pricing options under stochastic volatility. We derive these formulas and then apply them to the case where volatility is modelled as a continuous-time Markov chain, the so-called Markov regime-switching model. This model has been used previously in stochastic volatility modelling, but mostly with only states. We show how to use states without difficulty, and how larger number of states can be handled. Numerical illustrations are given, including the implied volatility curve in two- and three-state models. The curves have the ‘smile’ shape observed in practice. Journal: Applied Mathematical Finance Pages: 313-340 Issue: 4 Volume: 19 Year: 2012 Month: 6 X-DOI: 10.1080/1350486X.2011.624823 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.624823 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:4:p:313-340 Template-Type: ReDIF-Article 1.0 Author-Name: Moshe Levy Author-X-Name-First: Moshe Author-X-Name-Last: Levy Title: On the Spurious Correlation Between Sample Betas and Mean Returns Abstract: Cornerstone asset pricing models, such as capital asset pricing model (CAPM) and arbitrage pricing theory (APT), yield theoretical predictions about the relationship between expected returns and exposure to systematic risk, as measured by beta(s). Numerous studies have investigated the empirical validity of these models. We show that even if no relationship holds between true expected returns and betas in the population, the existence of low-probability extreme outcomes induces a spurious correlation between the sample means and the sample betas. Moreover, the magnitude of this purely spurious correlation is similar to the empirically documented correlation, and the regression slopes and intercepts are very similar as well. This result does not necessarily constitute evidence against the theoretical asset pricing models, but it does shed new light on previous empirical results, and it points to an issue that should be carefully considered in the empirical testing of these models. The analysis points to the dangers of relying on simple least squares regression for drawing conclusions about the validity of equilibrium pricing models. Journal: Applied Mathematical Finance Pages: 341-360 Issue: 4 Volume: 19 Year: 2012 Month: 9 X-DOI: 10.1080/1350486X.2011.624824 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.624824 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:4:p:341-360 Template-Type: ReDIF-Article 1.0 Author-Name: Lane P. Hughston Author-X-Name-First: Lane P. Author-X-Name-Last: Hughston Author-Name: Andrea Macrina Author-X-Name-First: Andrea Author-X-Name-Last: Macrina Title: Pricing Fixed-Income Securities in an Information-Based Framework Abstract: The purpose of this article is to introduce a class of information-based models for the pricing of fixed-income securities. We consider a set of continuous-time processes that describe the flow of information concerning market factors in a monetary economy. The nominal pricing kernel is assumed to be given at any specified time by a function of the values of information processes at that time. Using a change-of-measure technique, we derive explicit expressions for the prices of nominal discount bonds and deduce the associated dynamics of the short rate of interest and the market price of risk. The interest rate positivity condition is expressed as a differential inequality. An example that shows how the model can be calibrated to an arbitrary initial yield curve is presented. We proceed to model the price level, which is also taken at any specified time to be given by a function of the values of the information processes at that time. A simple model for a stochastic monetary economy is introduced in which the prices of the nominal discount bonds and inflation-linked notes can be expressed in terms of aggregate consumption and the liquidity benefit generated by the money supply. Journal: Applied Mathematical Finance Pages: 361-379 Issue: 4 Volume: 19 Year: 2012 Month: 9 X-DOI: 10.1080/1350486X.2011.631757 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.631757 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:4:p:361-379 Template-Type: ReDIF-Article 1.0 Author-Name: Paul Doust Author-X-Name-First: Paul Author-X-Name-Last: Doust Title: The Stochastic Intrinsic Currency Volatility Model: A Consistent Framework for Multiple FX Rates and Their Volatilities Abstract: The SABR and the Heston stochastic volatility models are widely used for foreign exchange (FX) option pricing. Although they are able to reproduce the market's volatility smiles and skews for single FX rates, they cannot be extended to model multiple FX rates in a consistent way. This is because when two FX rates with a common currency are described by either SABR or Heston processes, the stochastic process for the third FX rate associated with the three currencies will not be a SABR or a Heston process. A consistent description of the FX market should be symmetric so that all FX rates are described by the same type of stochastic process. This article presents a way of doing that using the concept of intrinsic currency values. To model FX volatility curves, the intrinsic currency framework is extended by allowing the volatility of each intrinsic currency value to be stochastic. This makes the framework more realistic, while preserving all FX market symmetries. The result is a new SABR-style option pricing formula and a model that can simultaneously be calibrated to the volatility smiles of all possible currency pairs under consideration. Consequently, it is more powerful than modelling the volatility curves of each currency pair individually and offers a methodology for comparing the volatility curves of different currency pairs against each other. One potential application of this is in the pricing of FX options, such as vanilla options on less liquid currency pairs. Given the volatilities of less liquid currencies against, for example, USD and EUR, the model could then be used to calculate the volatility smiles of those less liquid currencies against all other currencies. Journal: Applied Mathematical Finance Pages: 381-445 Issue: 5 Volume: 19 Year: 2012 Month: 11 X-DOI: 10.1080/1350486X.2011.626895 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.626895 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:5:p:381-445 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Chesney Author-X-Name-First: Marc Author-X-Name-Last: Chesney Author-Name: Luca Taschini Author-X-Name-First: Luca Author-X-Name-Last: Taschini Title: The Endogenous Price Dynamics of Emission Allowances and an Application to CO2 Option Pricing Abstract: Market mechanisms are increasingly being used as a tool for allocating somewhat scarce but unpriced rights and resources, and the European Emission Trading Scheme is an example. By means of dynamic optimization in the contest of firms covered by such environmental regulations, this article generates endogenously the price dynamics of emission permits under asymmetric information, allowing inter-temporal banking and borrowing. In the market, there are a finite number of firms and each firm's pollution emission follows an exogenously given stochastic process. We prove the discounted permit price is a martingale with respect to the relevant filtration. The model is solved numerically. Finally, a closed-form pricing formula for European-style options is derived. Journal: Applied Mathematical Finance Pages: 447-475 Issue: 5 Volume: 19 Year: 2012 Month: 11 X-DOI: 10.1080/1350486X.2011.639948 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.639948 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:5:p:447-475 Template-Type: ReDIF-Article 1.0 Author-Name: Gabriel G. Drimus Author-X-Name-First: Gabriel G. Author-X-Name-Last: Drimus Title: Options on Realized Variance in Log-OU Models Abstract: We study the pricing of options on realized variance in a general class of Log-OU (Ornstein--Ühlenbeck) stochastic volatility models. The class includes several important models proposed in the literature. Having as common feature the log-normal law of instantaneous variance, the application of standard Fourier--Laplace transform methods is not feasible. We derive extensions of Asian pricing methods, to obtain bounds, in particular, a very tight lower bound for options on realized variance. Journal: Applied Mathematical Finance Pages: 477-494 Issue: 5 Volume: 19 Year: 2012 Month: 11 X-DOI: 10.1080/1350486X.2011.639951 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.639951 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:5:p:477-494 Template-Type: ReDIF-Article 1.0 Author-Name: Pauline Barrieu Author-X-Name-First: Pauline Author-X-Name-Last: Barrieu Author-Name: Nadine Bellamy Author-X-Name-First: Nadine Author-X-Name-Last: Bellamy Author-Name: Jean-Michel Sahut Author-X-Name-First: Jean-Michel Author-X-Name-Last: Sahut Title: Assessing the Costs of Protection in a Context of Switching Stochastic Regimes Abstract: We consider the problem of cost assessment in the context of switching stochastic regimes. The dynamics of a given asset include a background noise, described by a Brownian motion and a random shock, the impact of which is characterized by changes in the coefficient diffusions. A particular economic agent that is directly exposed to variations in the underlying asset price, incurs some costs, , when the underlying asset price reaches a certain threshold, L. Ideally, the agent would make advance provision, or hedge, for these costs at time 0. We evaluate the amount of provision, or the hedging premium, , for these costs in the disrupted environment, with changes in the regime for a given time horizon, and analyse the sensitivity of this amount to possible model misspecifications. Journal: Applied Mathematical Finance Pages: 495-511 Issue: 6 Volume: 19 Year: 2012 Month: 12 X-DOI: 10.1080/1350486X.2011.642615 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.642615 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:6:p:495-511 Template-Type: ReDIF-Article 1.0 Author-Name: Hans-Peter Bermin Author-X-Name-First: Hans-Peter Author-X-Name-Last: Bermin Title: Bonds and Options in Exponentially Affine Bond Models Abstract: In this article we apply the Flesaker--Hughston approach to invert the yield curve and to price various options by letting the randomness in the economy be driven by a process closely related to the short rate, called the abstract short rate. This process is a pure deterministic translation of the short rate itself, and we use the deterministic shift to calibrate the models to the initial yield curve. We show that we can solve for the shift needed in closed form by transforming the problem to a new probability measure. Furthermore, when the abstract short rate follows a Cox--Ingersoll--Ross (CIR) process we compute bond option and swaption prices in closed form. We also propose a short-rate specification under the risk-neutral measure that allows the yield curve to be inverted and is consistent with the CIR dynamics for the abstract short rate, thus giving rise to closed form bond option and swaption prices. Journal: Applied Mathematical Finance Pages: 513-534 Issue: 6 Volume: 19 Year: 2012 Month: 12 X-DOI: 10.1080/1350486X.2011.646505 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.646505 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:6:p:513-534 Template-Type: ReDIF-Article 1.0 Author-Name: Álvaro Cartea Author-X-Name-First: Álvaro Author-X-Name-Last: Cartea Author-Name: Dimitrios Karyampas Author-X-Name-First: Dimitrios Author-X-Name-Last: Karyampas Title: Assessing the Performance of Different Volatility Estimators: A Monte Carlo Analysis Abstract: We test the performance of different volatility estimators that have recently been proposed in the literature and have been designed to deal with problems arising when ultra high-frequency data are employed: microstructure noise and price discontinuities. Our goal is to provide an extensive simulation analysis for different levels of noise and frequency of jumps to compare the performance of the proposed volatility estimators. We conclude that the maximum likelihood estimator filter (MLE-F), a two-step parametric volatility estimator proposed by Cartea and Karyampas (2011a; The relationship between the volatility returns and the number of jumps in financial markets, SSRN eLibrary, Working Paper Series, SSRN), outperforms most of the well-known high-frequency volatility estimators when different assumptions about the path properties of stock dynamics are used. Journal: Applied Mathematical Finance Pages: 535-552 Issue: 6 Volume: 19 Year: 2012 Month: 12 X-DOI: 10.1080/1350486X.2011.646513 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.646513 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:6:p:535-552 Template-Type: ReDIF-Article 1.0 Author-Name: Joanne E. Kennedy Author-X-Name-First: Joanne E. Author-X-Name-Last: Kennedy Author-Name: Subhankar Mitra Author-X-Name-First: Subhankar Author-X-Name-Last: Mitra Author-Name: Duy Pham Author-X-Name-First: Duy Author-X-Name-Last: Pham Title: On the Approximation of the SABR Model: A Probabilistic Approach Abstract: In this article, we derive a probabilistic approximation for three different versions of the SABR model: Normal, Log-Normal and a displaced diffusion version for the general case. Specifically, we focus on capturing the terminal distribution of the underlying process (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a variety of parameters that cover the long-dated options and highly stress market condition. This is a different feature from other current approaches that rely on the assumption of very small total volatility and usually fail for longer than 10 years maturity or large volatility of volatility (Volvol). Journal: Applied Mathematical Finance Pages: 553-586 Issue: 6 Volume: 19 Year: 2012 Month: 12 X-DOI: 10.1080/1350486X.2011.646523 File-URL: http://hdl.handle.net/10.1080/1350486X.2011.646523 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:19:y:2012:i:6:p:553-586 Template-Type: ReDIF-Article 1.0 Author-Name: Robert J. Elliott Author-X-Name-First: Robert J. Author-X-Name-Last: Elliott Author-Name: Tak Kuen Siu Author-X-Name-First: Tak Kuen Author-X-Name-Last: Siu Title: Option Pricing and Filtering with Hidden Markov-Modulated Pure-Jump Processes Abstract: This article discusses the pricing of derivatives in a continuous-time, hidden Markov-modulated, pure-jump asset price model. The hidden Markov chain modulating the pure-jump asset price model describes the evolution of the hidden state of an economy over time. The market model is incomplete. We employ a version of the Esscher transform to select a price kernel for valuation. We derive a valuation formula for European options using a Fourier transform and the correlation theorem. This formula depends on the hidden Markov chain. It is then estimated using a robust filter of the chain. Journal: Applied Mathematical Finance Pages: 1-25 Issue: 1 Volume: 20 Year: 2013 Month: 3 X-DOI: 10.1080/1350486X.2012.655929 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.655929 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:1:p:1-25 Template-Type: ReDIF-Article 1.0 Author-Name: Svetlana Boyarchenko Author-X-Name-First: Svetlana Author-X-Name-Last: Boyarchenko Author-Name: Sergei LevendorskiĬ Author-X-Name-First: Sergei Author-X-Name-Last: LevendorskiĬ Title: American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations Abstract: We consider the Heston model with the stochastic interest rate of Cox--Ingersoll--Ross (CIR) type and more general models with stochastic volatility and interest rates depending on two CIR-factors; the price, volatility and interest rate may correlate. Time-derivative and infinitesimal generator of the process for factors that determine the dynamics of the interest rate and/or volatility are discretized. The result is a sequence of embedded perpetual options arising in the time discretization of a Markov-modulated L�vy model. Options in this sequence are solved using an iteration method based on the Wiener--Hopf factorization. Typical shapes of the early exercise boundary are shown, and good agreement of option prices with prices calculated with the Longstaff--Schwartz method and Medvedev--Scaillet asymptotic method is demonstrated. Journal: Applied Mathematical Finance Pages: 26-49 Issue: 1 Volume: 20 Year: 2013 Month: 3 X-DOI: 10.1080/1350486X.2012.655935 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.655935 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:1:p:26-49 Template-Type: ReDIF-Article 1.0 Author-Name: Ryosuke Ishii Author-X-Name-First: Ryosuke Author-X-Name-Last: Ishii Author-Name: Katsumasa Nishide Author-X-Name-First: Katsumasa Author-X-Name-Last: Nishide Title: Concentrated Equilibrium and Intraday Patterns in Financial Markets Abstract: We introduce endogenous participation of market makers into a Kyle-type model with long-lived asymmetric information. In our model with plausible parameter values, the trading volume and price volatility show a U-shaped intraday pattern, often observed in actual financial markets. It will be shown that the pattern is caused not only by the trading behaviour of liquidity traders but also by that of market makers. Our findings shed new light on the stylized fact of the trade concentration at the opening and closing periods. Journal: Applied Mathematical Finance Pages: 50-68 Issue: 1 Volume: 20 Year: 2013 Month: 3 X-DOI: 10.1080/1350486X.2012.656996 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.656996 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:1:p:50-68 Template-Type: ReDIF-Article 1.0 Author-Name: Noufel Frikha Author-X-Name-First: Noufel Author-X-Name-Last: Frikha Author-Name: Vincent Lemaire Author-X-Name-First: Vincent Author-X-Name-Last: Lemaire Title: Joint Modelling of Gas and Electricity Spot Prices Abstract: The recent liberalization of electricity and gas markets has resulted in the growth of energy exchanges and modelling problems. In this article, we jointly model gas and electricity spot prices using a mean-reverting model that fits the correlation structures for the two commodities. The dynamics are based on Ornstein processes with parameterized diffusion coefficients. Moreover, using the empirical distributions of the spot prices, we derive a class of such parameterized diffusions that captures the most salient statistical properties: stationarity, spikes and heavy-tailed distributions. The associated calibration procedure is based on standard and efficient statistical tools. We calibrate the model on French market for electricity and on UK market for gas, and then we simulate some trajectories that reproduce well the observed prices behaviour. Finally, we illustrate the importance of the correlation structure and of the presence of spikes by measuring the risk on a power plant portfolio. Journal: Applied Mathematical Finance Pages: 69-93 Issue: 1 Volume: 20 Year: 2013 Month: 3 X-DOI: 10.1080/1350486X.2012.658220 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.658220 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:1:p:69-93 Template-Type: ReDIF-Article 1.0 Author-Name: Mia Hinnerich Author-X-Name-First: Mia Author-X-Name-Last: Hinnerich Title: Pricing Equity Swaps in an Economy with Jumps Abstract: Empirical evidence confirms that asset price processes exhibit jumps and that asset returns are not Gaussian. We provide a pricing model for equity swaps including quanto equity swaps for a non-Gaussian market. The market is driven by a general marked point process as well as by a standard multidimensional Wiener process. In order to obtain closed-form solutions of the swap values, we assume that all parameters in the asset price processes are deterministic, but possibly functions of time. We derive swap prices using martingale methods rather than replicating portfolios, and we show how to calculate the convexity correction term analytically. Our results are an extension of the results of Liao and Wang (2003; Pricing models of equity swaps, The Journal of Futures Markets, 23(8), pp. 751--772). The martingale method is the key that enables the extension. Journal: Applied Mathematical Finance Pages: 94-117 Issue: 2 Volume: 20 Year: 2013 Month: 4 X-DOI: 10.1080/1350486X.2012.659556 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.659556 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:2:p:94-117 Template-Type: ReDIF-Article 1.0 Author-Name: Matheus R. Grasselli Author-X-Name-First: Matheus R. Author-X-Name-Last: Grasselli Author-Name: Cesar Gómez Author-X-Name-First: Cesar Author-X-Name-Last: Gómez Title: Stock Loans in Incomplete Markets Abstract: A stock loan is a contract whereby a stockholder uses shares as collateral to borrow money from a bank or financial institution. In Xia and Zhou (2007, Stock loans, Mathematical Finance, 17(2), pp. 307--317), this contract is modelled as a perpetual American option with a time-varying strike and analysed in detail within a risk-neutral framework. In this paper, we extend the valuation of such loans to an incomplete market setting, which takes into account the natural trading restrictions faced by the client. When the maturity of the loan is infinite, we use a time-homogeneous utility maximization problem to obtain an exact formula for the value of the loan fee to be charged by the bank. For loans of finite maturity, we characterize the fee using variational inequality techniques. In both cases, we show analytically how the fee varies with the model parameters and illustrate the results numerically. Journal: Applied Mathematical Finance Pages: 118-136 Issue: 2 Volume: 20 Year: 2013 Month: 4 X-DOI: 10.1080/1350486X.2012.660318 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.660318 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:2:p:118-136 Template-Type: ReDIF-Article 1.0 Author-Name: Clive G. Bowsher Author-X-Name-First: Clive G. Author-X-Name-Last: Bowsher Author-Name: Roland Meeks Author-X-Name-First: Roland Author-X-Name-Last: Meeks Title: Stationary and Nonstationary Behaviour of the Term Structure: A Nonparametric Characterization Abstract: We provide simple nonparametric conditions for the order of integration of the term structure of zero-coupon yields. A principal benchmark model studied is one with a limiting yield and limiting term premium, and in which the logarithmic expectations theory (ET) holds. By considering a yield curve with a complete term structure of bond maturities, a linear vector autoregressive process is constructed that provides an arbitrarily accurate representation of the yield curve as its cross-sectional dimension goes to infinity. We use this to provide parsimonious conditions for the integration order of interest rates in terms of the cross-sectional rate of convergence of the innovations to yields, as . The yield curve is stationary if and only if converges a.s., or equivalently the innovations (shocks) to the logarithm of the bond prices converge a.s. Otherwise yields are nonstationary and I(1) in the benchmark model, an integration order greater than 1 being ruled out by the a.s. convergence of as . A necessary but not sufficient condition for stationarity is that the limiting yield is constant over time. Our results therefore imply the need usually to adopt an I(1) framework when using the ET. We provide ET-consistent yield curve forecasts, new means to evaluate the ET and insight into connections between the dynamics and the long maturity end of the term structure. Journal: Applied Mathematical Finance Pages: 137-166 Issue: 2 Volume: 20 Year: 2013 Month: 4 X-DOI: 10.1080/1350486X.2012.666120 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.666120 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:2:p:137-166 Template-Type: ReDIF-Article 1.0 Author-Name: Koichi Matsumoto Author-X-Name-First: Koichi Author-X-Name-Last: Matsumoto Title: Option Replication in Discrete Time with Illiquidity Abstract: This article studies a replication of a contingent claim in an illiquid market. We represent the liquidity as a supply curve in a discrete time model. Because the trade price of the illiquid asset is a function of the trade size in this model, it is important whether the contingent claim is physically settled or settled in cash. In both cases, we give a condition where a replication strategy exists uniquely and show some properties of the replication strategy. Further we analyse the liquidity cost numerically. Journal: Applied Mathematical Finance Pages: 167-190 Issue: 2 Volume: 20 Year: 2013 Month: 4 X-DOI: 10.1080/1350486X.2012.675161 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.675161 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:2:p:167-190 Template-Type: ReDIF-Article 1.0 Author-Name: Massimo Costabile Author-X-Name-First: Massimo Author-X-Name-Last: Costabile Author-Name: Ivar Massabó Author-X-Name-First: Ivar Author-X-Name-Last: Massabó Author-Name: Emilio Russo Author-X-Name-First: Emilio Author-X-Name-Last: Russo Title: A Path-Independent Humped Volatility Model for Option Pricing Abstract: This article presents a path-independent model for evaluating interest-sensitive claims in a Heath--Jarrow--Morton (1992, Bond pricing and the term structure of interest rates: a new methodology for contingent claims valuation, Econometrica, 60, pp. 77--105) framework, when the volatility structure of forward rates shows the deterministic and stationary humped shape analysed by Ritchken and Chuang (2000, Interest rate option pricing with volatility humps, Review of Derivatives Research, 3(3), pp. 237--262). In our analysis, the evolution of the term structure is captured by a one-factor short rate process with drift depending on a three-dimensional state variable Markov process. We develop a lattice to discretize the dynamics of each variable appearing in the short rate process, and establish a three-variate reconnecting tree to compute interest-sensitive claim prices. The proposed approach makes the evaluation problem path-independent, thus overcoming the computational difficulties in managing path-dependent variables as it happens in the Ritchken--Chuang (2000, Interest rate option pricing with volatility humps, Review of Derivatives Research, 3(3), pp. 237--262) model. Journal: Applied Mathematical Finance Pages: 191-210 Issue: 3 Volume: 20 Year: 2013 Month: 7 X-DOI: 10.1080/1350486X.2012.676798 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.676798 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:3:p:191-210 Template-Type: ReDIF-Article 1.0 Author-Name: Akira Yamazaki Author-X-Name-First: Akira Author-X-Name-Last: Yamazaki Title: Exponential L�vy Models Extended by a Jump to Default Abstract: This article proposes a new dynamically consistent framework for joint valuation of equity derivatives and credit products, in which uncertainty of the economy is represented by L�vy processes. In the framework, the pre-default stock price of a given firm is presented by an extended exponential L�vy model, while the default arrival rate is presented by the Cox proportional hazard model with stochastic covariates driven by L�vy processes. Under the model, we find the solution of the pricing generator for evaluating equity and credit derivatives, and we derive the pricing formulas of equity call options and credit default swaps by utilizing the pricing generator. In the numerical examples, setting the variance gamma (VG) process and the Brownian motion as driving factors of the model, we compute term structure of credit default swaps and equity implied volatility skews. We also examine the impact of the convexity adjustment on term structure of credit spreads both analytically and numerically. Journal: Applied Mathematical Finance Pages: 211-228 Issue: 3 Volume: 20 Year: 2013 Month: 7 X-DOI: 10.1080/1350486X.2012.677222 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.677222 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:3:p:211-228 Template-Type: ReDIF-Article 1.0 Author-Name: Nabil Tahani Author-X-Name-First: Nabil Author-X-Name-Last: Tahani Title: Exotic Geometric Average Options Pricing under Stochastic Volatility Abstract: This article derives semi-analytical pricing formulae for geometric average options (GAOs) within a stochastic volatility framework. Assuming a general mean reverting process for the underlying asset and a square-root process for the volatility, the cross-moment generating function is derived and the cumulative probabilities are recovered using the Gauss--Laguerre quadrature rule. Fixed and floating strikes as well as other exotic GAO on different assets such as stocks, currency exchange rates and interest rates are derived. The approach is found to be very accurate and efficient. Journal: Applied Mathematical Finance Pages: 229-245 Issue: 3 Volume: 20 Year: 2013 Month: 7 X-DOI: 10.1080/1350486X.2012.678735 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.678735 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:3:p:229-245 Template-Type: ReDIF-Article 1.0 Author-Name: Agatha Murgoci Author-X-Name-First: Agatha Author-X-Name-Last: Murgoci Title: Vulnerable Derivatives and Good Deal Bounds: A Structural Model Abstract: We price vulnerable derivatives -- i.e. derivatives where the counterparty may default. These are basically the derivatives traded on the over-the-counter (OTC) markets. Default is modelled in a structural framework. The technique employed for pricing is good deal bounds (GDBs). The method imposes a new restriction in the arbitrage free model by setting upper bounds on the Sharpe ratios (SRs) of the assets. The potential prices that are eliminated represent unreasonably good deals. The constraint on the SR translates into a constraint on the stochastic discount factor. Thus, tight pricing bounds can be obtained. We provide a link between the objective probability measure and the range of potential risk-neutral measures, which has an intuitive economic meaning. We also provide tight pricing bounds for European calls and show how to extend the call formula to pricing other financial products in a consistent way. Finally, we numerically analyse the behaviour of the good deal pricing bounds. Journal: Applied Mathematical Finance Pages: 246-263 Issue: 3 Volume: 20 Year: 2013 Month: 7 X-DOI: 10.1080/1350486X.2012.681964 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.681964 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:3:p:246-263 Template-Type: ReDIF-Article 1.0 Author-Name: Alexander Schied Author-X-Name-First: Alexander Author-X-Name-Last: Schied Title: Robust Strategies for Optimal Order Execution in the Almgren--Chriss Framework Abstract: Assuming geometric Brownian motion as unaffected price process , Gatheral and Schied (2011; Optimal trade execution under geometric Brownian motion in the Almgren and Chriss framework, International Journal of Theoretical and Applied Finance, 14, pp. 353--368) derived a strategy for optimal order execution that reacts in a sensible manner on market changes but can still be computed in closed form. Here, we will investigate the robustness of this strategy with respect to misspecification of the law of . We prove the surprising result that the strategy remains optimal whenever is a square-integrable martingale. We then analyse the optimization criterion of Gatheral and Schied (2011) in the case in which is any square-integrable semimartingale and we give a closed-form solution to this problem. As a corollary, we find an explicit solution to the problem of minimizing the expected liquidation costs when the unaffected price process is a square-integrable semimartingale. The solutions to our problems are found by stochastically solving a finite-fuel control problem without assumptions of Markovianity. Journal: Applied Mathematical Finance Pages: 264-286 Issue: 3 Volume: 20 Year: 2013 Month: 7 X-DOI: 10.1080/1350486X.2012.683963 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.683963 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:3:p:264-286 Template-Type: ReDIF-Article 1.0 Author-Name: Heikki Tikanmäki Author-X-Name-First: Heikki Author-X-Name-Last: Tikanmäki Title: Robust Hedging and Pathwise Calculus Abstract: We study the connections of two different pathwise hedging approaches. These approaches are Bender-Sottinen-Valkeila (BSV) by Bender et al. (2008, Pricing by hedging and no-arbitrage beyond semimartingales, finance and stochastics, 12(4), pp. 441--468.) and Cont and Fourni� (CF) by Cont and Fourni� (2010, Change of variable formulas for non-anticipative functionals on path space, Journal of Functional Analysis, 259(4), pp. 1043--1072; in press, Functional Ito calculus and stochastic integral representation of martingales, Annals of probability). We prove that both approaches give the same pathwise hedges, whenever both of the strategies exist. We also prove BSV-type robust replication result for CF strategies. Journal: Applied Mathematical Finance Pages: 287-303 Issue: 3 Volume: 20 Year: 2013 Month: 7 X-DOI: 10.1080/1350486X.2012.725978 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.725978 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:3:p:287-303 Template-Type: ReDIF-Article 1.0 Author-Name: Traian A. Pirvu Author-X-Name-First: Traian A. Author-X-Name-Last: Pirvu Author-Name: Huayue Zhang Author-X-Name-First: Huayue Author-X-Name-Last: Zhang Title: Utility Indifference Pricing: A Time Consistent Approach Abstract: This article considers the optimal portfolio selection problem in a dynamic multi-period stochastic framework with regime switching. The risk preferences are of exponential (CARA) type with an absolute coefficient of risk aversion that changes with the regime. The market model is incomplete and there are two risky assets: tradable and non-tradable. In this context, the optimal investment strategies are time inconsistent. Consequently, the subgame perfect equilibrium strategies are considered. The utility indifference ask price of a contingent claim written on the risky assets is computed through an indifference valuation algorithm. By running numerical experiments, we examine how this price varies in response to changes in model parameters. Journal: Applied Mathematical Finance Pages: 304-326 Issue: 4 Volume: 20 Year: 2013 Month: 9 X-DOI: 10.1080/1350486X.2012.700575 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.700575 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:4:p:304-326 Template-Type: ReDIF-Article 1.0 Author-Name: Linus Kaisajuntti Author-X-Name-First: Linus Author-X-Name-Last: Kaisajuntti Title: A Parametric n-Dimensional Markov-Functional Model in the Terminal Measure Abstract: This article develops and tests an n-dimensional Markov-functional interest rate model in the terminal measure based on parametric functional forms of exponential type. The parametric functional forms enable analytical expressions for forward discount bonds and forward LIBORs at all times and allows for calibration of the model to caplet prices given by a displaced diffusion Black model. The analytical expressions of the model provide a theoretical tool for understanding the structure of standard Markov-functional models (MFMs) as well as comparisons with the LIBOR market model (LMM). In particular, it is shown that for ‘typical’ market data the model is close enough to the LMM to be able to calibrate using the LMM calibration set-up and machinery. This provides further information about the similarities (as well as some of the differences) between MFM and LMM. The parametric n-dimensional MFM may be used for products that require high-dimensional models for appropriate pricing and risk management. When compared with an n-factor LMM, it has the virtue of being (much) faster for certain types of products. Journal: Applied Mathematical Finance Pages: 327-358 Issue: 4 Volume: 20 Year: 2013 Month: 9 X-DOI: 10.1080/1350486X.2012.708600 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.708600 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:4:p:327-358 Template-Type: ReDIF-Article 1.0 Author-Name: Cyrus Seera Ssebugenyi Author-X-Name-First: Cyrus Seera Author-X-Name-Last: Ssebugenyi Author-Name: Ivivi Joseph Mwaniki Author-X-Name-First: Ivivi Joseph Author-X-Name-Last: Mwaniki Author-Name: Virginie S. Konlack Author-X-Name-First: Virginie S. Author-X-Name-Last: Konlack Title: On the Minimal Entropy Martingale Measure and Multinomial Lattices with Cumulants Abstract: In this article, we describe with relevant examples based on empirical data how to use the minimal entropy martingale measure (MEMM) to price European and American Options in multinomial lattices which take into account cumulants information. For trinomial lattices, we show that minimal entropy prices are close to results obtained using the Black and Scholes option pricing formula. For pentanomial lattices, minimal entropy prices are close to results obtained under the mean-correcting martingale measure using the discrete Fourier transform. The MEMM is very easy to compute and is therefore a good candidate for option pricing in multinomial lattices. Journal: Applied Mathematical Finance Pages: 359-379 Issue: 4 Volume: 20 Year: 2013 Month: 9 X-DOI: 10.1080/1350486X.2012.714226 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.714226 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:4:p:359-379 Template-Type: ReDIF-Article 1.0 Author-Name: Griselda Deelstra Author-X-Name-First: Griselda Author-X-Name-Last: Deelstra Author-Name: Gr�gory Ray�e Author-X-Name-First: Gr�gory Author-X-Name-Last: Ray�e Title: Local Volatility Pricing Models for Long-Dated FX Derivatives Abstract: We study the local volatility function in the foreign exchange (FX) market, where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility on the FX option's market. Then, we study an extension to obtain a more general volatility model and propose a calibration method for the local volatility associated with this model. Journal: Applied Mathematical Finance Pages: 380-402 Issue: 4 Volume: 20 Year: 2013 Month: 9 X-DOI: 10.1080/1350486X.2012.723516 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.723516 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:4:p:380-402 Template-Type: ReDIF-Article 1.0 Author-Name: Kawee Numpacharoen Author-X-Name-First: Kawee Author-X-Name-Last: Numpacharoen Author-Name: Kornkanok Bunwong Author-X-Name-First: Kornkanok Author-X-Name-Last: Bunwong Title: Boundaries of Correlation Adjustment with Applications to Financial Risk Management Abstract: In recent years, stress testing has become a regulatory requirement for risk assessment in financial institutions. To perform stress testing in multi-asset case, adjusting the correlation matrix to an extreme level is an important process. With a larger matrix, it is more difficult to choose the right correlation coefficients such that the newly adjusted correlation matrix is still valid. In this article, we present a systematic way to obtain the boundaries of a correlation matrix for both single stress and multiple stress cases, which can help determine how much the correlation should be adjusted in the first place. Journal: Applied Mathematical Finance Pages: 403-414 Issue: 4 Volume: 20 Year: 2013 Month: 9 X-DOI: 10.1080/1350486X.2012.723517 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.723517 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:4:p:403-414 Template-Type: ReDIF-Article 1.0 Author-Name: Tse Author-X-Name-First: Author-X-Name-Last: Tse Author-Name: Forsyth Author-X-Name-First: Author-X-Name-Last: Forsyth Author-Name: Kennedy Author-X-Name-First: Author-X-Name-Last: Kennedy Author-Name: Windcliff Author-X-Name-First: Author-X-Name-Last: Windcliff Title: Comparison Between the Mean-Variance Optimal and the Mean-Quadratic-Variation Optimal Trading Strategies Abstract: We compare optimal liquidation policies in continuous time in the presence of trading impact using numerical solutions of Hamilton--Jacobi--Bellman (HJB) partial differential equations (PDEs). In particular, we compare the time-consistent mean-quadratic-variation strategy with the time-inconsistent (pre-commitment) mean-variance strategy. We show that the two different risk measures lead to very different strategies and liquidation profiles. In terms of the optimal trading velocities, the mean-quadratic-variation strategy is much less sensitive to changes in asset price and varies more smoothly. In terms of the liquidation profiles, the mean-variance strategy is much more variable, although the mean liquidation profiles for the two strategies are surprisingly similar. On a numerical note, we show that using an interpolation scheme along a parametric curve in conjunction with the semi-Lagrangian method results in significantly better accuracy than standard axis-aligned linear interpolation. We also demonstrate how a scaled computational grid can improve solution accuracy. Journal: Applied Mathematical Finance Pages: 415-449 Issue: 5 Volume: 20 Year: 2013 Month: 11 X-DOI: 10.1080/1350486X.2012.755817 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.755817 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:5:p:415-449 Template-Type: ReDIF-Article 1.0 Author-Name: Elliott Author-X-Name-First: Author-X-Name-Last: Elliott Author-Name: van der Hoek Author-X-Name-First: Author-X-Name-Last: van der Hoek Title: Default Times in a Continuous Time Markov Chain Economy Abstract: A continuous time financial market is considered where randomness is modelled by a finite state Markov chain. Using the chain, a stochastic discount factor is defined. The probability distributions of default times are shown to be given by solutions of a system of coupled partial differential equations. Journal: Applied Mathematical Finance Pages: 450-460 Issue: 5 Volume: 20 Year: 2013 Month: 11 X-DOI: 10.1080/1350486X.2012.755825 File-URL: http://hdl.handle.net/10.1080/1350486X.2012.755825 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:5:p:450-460 Template-Type: ReDIF-Article 1.0 Author-Name: Eberlein Author-X-Name-First: Author-X-Name-Last: Eberlein Author-Name: Madan Author-X-Name-First: Author-X-Name-Last: Madan Author-Name: Pistorius Author-X-Name-First: Author-X-Name-Last: Pistorius Author-Name: Yor Author-X-Name-First: Author-X-Name-Last: Yor Title: A Simple Stochastic Rate Model for Rate Equity Hybrid Products Abstract: A positive spot rate model driven by a gamma process and correlated with equity is introduced and calibrated via closed forms for the joint characteristic function for the rate r, its integral y and the logarithm of the stock price s under the T-forward measure. The law of the triple is expressed as a nonlinear transform of three independent processes, a gamma process, a variance gamma process and a Wiener integral with respect to the Dirichlet process. The generalized Stieltjes transform of the Wiener integral with respect to the Dirichlet process is derived in closed form. Inversion of this transform using Schwarz (2005, The generalized Stieltjes transform and its inverse, Journal of Mathematical Physics, 46(1), doi: 10.1063/1.1825077) makes large step simulations possible. Valuing functions are built and hedged using quantization and high dimensional interpolation methods. The hedging objective is taken to be capital minimization as described by Carr, Madan and Vicente Alvarez (2011, Markets, profits, capital, leverage and returns, Journal of Risk, 14(1), pp. 95--122). Journal: Applied Mathematical Finance Pages: 461-488 Issue: 5 Volume: 20 Year: 2013 Month: 11 X-DOI: 10.1080/1350486X.2013.770240 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.770240 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:5:p:461-488 Template-Type: ReDIF-Article 1.0 Author-Name: Hofer Author-X-Name-First: Author-X-Name-Last: Hofer Author-Name: Mayer Author-X-Name-First: Author-X-Name-Last: Mayer Title: Pricing and Hedging of Lookback Options in Hyper-exponential Jump Diffusion Models Abstract: In this article, we consider the problem of pricing lookback options in certain exponential L�vy market models. While in the classic Black-Scholes models the price of such options can be calculated in closed form, for more general asset price model, one typically has to rely on (rather time-intense) Monte-Carlo or partial (integro)-differential equation (P(I)DE) methods. However, for L�vy processes with double exponentially distributed jumps, the lookback option price can be expressed as one-dimensional Laplace transform (cf. Kou, S. G., Petrella, G., & Wang, H. (2005). Pricing path-dependent options with jump risk via Laplace transforms. The Kyoto Economic Review, 74(9), 1--23.). The key ingredient to derive this representation is the explicit availability of the first passage time distribution for this particular L�vy process, which is well-known also for the more general class of hyper-exponential jump diffusions (HEJDs). In fact, Jeannin and Pistorius (Jeannin, M., & Pistorius, M. (2010). A transform approach to calculate prices and Greeks of barrier options driven by a class of L�vy processes. Quntitative Finance, 10(6), 629--644.) were able to derive formulae for the Laplace transformed price of certain barrier options in market models described by HEJD processes. Here, we similarly derive the Laplace transforms of floating and fixed strike lookback option prices and propose a numerical inversion scheme, which allows, like Fourier inversion methods for European vanilla options, the calculation of lookback options with different strikes in one shot. Additionally, we give semi-analytical formulae for several Greeks of the option price and discuss a method of extending the proposed method to generalized hyper-exponential (as e.g. NIG or CGMY) models by fitting a suitable HEJD process. Finally, we illustrate the theoretical findings by some numerical experiments. Journal: Applied Mathematical Finance Pages: 489-511 Issue: 5 Volume: 20 Year: 2013 Month: 11 X-DOI: 10.1080/1350486X.2013.774985 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.774985 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:5:p:489-511 Template-Type: ReDIF-Article 1.0 Author-Name: �lvaro Cartea Author-X-Name-First: �lvaro Author-X-Name-Last: Cartea Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Modelling Asset Prices for Algorithmic and High-Frequency Trading Abstract: Algorithmic trading (AT) and high-frequency (HF) trading, which are responsible for over 70% of US stocks trading volume, have greatly changed the microstructure dynamics of tick-by-tick stock data. In this article, we employ a hidden Markov model to examine how the intraday dynamics of the stock market have changed and how to use this information to develop trading strategies at high frequencies. In particular, we show how to employ our model to submit limit orders to profit from the bid-ask spread, and we also provide evidence of how HF traders may profit from liquidity incentives (liquidity rebates). We use data from February 2001 and February 2008 to show that while in 2001 the intraday states with the shortest average durations (waiting time between trades) were also the ones with very few trades, in 2008 the vast majority of trades took place in the states with the shortest average durations. Moreover, in 2008, the states with the shortest durations have the smallest price impact as measured by the volatility of price innovations. Journal: Applied Mathematical Finance Pages: 512-547 Issue: 6 Volume: 20 Year: 2013 Month: 12 X-DOI: 10.1080/1350486X.2013.771515 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.771515 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:6:p:512-547 Template-Type: ReDIF-Article 1.0 Author-Name: Cassio Neri Author-X-Name-First: Cassio Author-X-Name-Last: Neri Author-Name: Lorenz Schneider Author-X-Name-First: Lorenz Author-X-Name-Last: Schneider Title: A Family of Maximum Entropy Densities Matching Call Option Prices Abstract: We investigate the position of the Buchen-Kelly density (Peter W. Buchen and Michael Kelly. The maximum entropy distribution of an asset inferred from option prices. Journal of Financial and Quantitative Analysis, 31(1), 143-159, March 1996.) in the family of entropy maximizing densities from Neri and Schneider (Maximum entropy distributions inferred from option portfolios on an asset. Finance and Stochastics, 16(2), 293-318, April 2012.), which all match European call option prices for a given maturity observed in the market. Using the Legendre transform, which links the entropy function and the cumulant generating function, we show that it is both the unique continuous density in this family and the one with the greatest entropy. We present a fast root-finding algorithm that can be used to calculate the Buchen-Kelly density and give upper boundaries for three different discrepancies that can be used as convergence criteria. Given the call prices, arbitrage-free digital prices at the same strikes can only move within upper and lower boundaries given by left and right call spreads. As the number of call prices increases, these bounds become tighter, and we give two examples where the densities converge to the Buchen-Kelly density in the sense of relative entropy. The method presented here can also be used to interpolate between call option prices, and we compare it to a method proposed by Kahal� (An arbitrage-free interpolation of volatilities. Risk, 17(5), 102-106, May 2004). Orozco Rodriguez and Santosa (Estimation of asset distributions from option prices: Analysis and regularization. SIAM Journal on Financial Mathematics, 3(1), 374-401, 2012.) have produced examples in which the Buchen-Kelly algorithm becomes numerically unstable, and we use these as test cases to show that the algorithm given here remains stable and leads to good results. Journal: Applied Mathematical Finance Pages: 548-577 Issue: 6 Volume: 20 Year: 2013 Month: 12 X-DOI: 10.1080/1350486X.2013.780769 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.780769 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:6:p:548-577 Template-Type: ReDIF-Article 1.0 Author-Name: Matteo Ortisi Author-X-Name-First: Matteo Author-X-Name-Last: Ortisi Author-Name: Valerio Zuccolo Author-X-Name-First: Valerio Author-X-Name-Last: Zuccolo Title: From Minority Game to Black&Scholes Pricing Abstract: In this paper, we study the continuum time dynamics of a stock in a market where agents behaviour is modelled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the Black&Scholes formula the calibration of both the Minority Game and the Grand Canonical Minority Game, by means of their characteristic parameters, is performed. We conclude that for both games the asymmetric phase with characteristic parameters close to critical ones is coherent with options implied volatility market. Journal: Applied Mathematical Finance Pages: 578-598 Issue: 6 Volume: 20 Year: 2013 Month: 12 X-DOI: 10.1080/1350486X.2013.787246 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.787246 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:6:p:578-598 Template-Type: ReDIF-Article 1.0 Author-Name: Bing Lu Author-X-Name-First: Bing Author-X-Name-Last: Lu Title: Optimal Selling of an Asset with Jumps Under Incomplete Information Abstract: We study the optimal liquidation strategy of an asset with price process satisfying a jump diffusion model with unknown jump intensity. It is assumed that the intensity takes one of two given values, and we have an initial estimate for the probability of both of them. As time goes by, by observing the price fluctuations, we can thus update our beliefs about the probabilities for the intensity distribution. We formulate an optimal stopping problem describing the optimal liquidation problem. It is shown that the optimal strategy is to liquidate the first time the point process falls below (goes above) a certain time-dependent boundary. Journal: Applied Mathematical Finance Pages: 599-610 Issue: 6 Volume: 20 Year: 2013 Month: 12 X-DOI: 10.1080/1350486X.2013.810462 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.810462 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:20:y:2013:i:6:p:599-610 Template-Type: ReDIF-Article 1.0 Author-Name: Wendong Zheng Author-X-Name-First: Wendong Author-X-Name-Last: Zheng Author-Name: Yue Kuen Kwok Author-X-Name-First: Yue Kuen Author-X-Name-Last: Kwok Title: Saddlepoint Approximation Methods for Pricing Derivatives on Discrete Realized Variance Abstract: We consider the saddlepoint approximation methods for pricing derivatives whose payoffs depend on the discrete realized variance of the underlying price process of a risky asset. Most of the earlier pricing models of variance products and volatility derivatives use the quadratic variation approximation as the continuous limit of the discrete realized variance. However, the corresponding discretization error may become significant for short-maturity derivatives. Under L�vy models and stochastic volatility models with jumps, we manage to obtain the saddlepoint approximation formulas for pricing variance products and volatility derivatives using the small time asymptotic approximation of the Laplace transform of the discrete realized variance. As an alternative approach, we also develop the conditional saddlepoint approximation method based on a given simulated stochastic variance path via Monte Carlo simulation. This analytic-simulation approach reduces the dimensionality of the simulation of the discrete variance derivatives; and in some cases, the simulation procedure of the realized variance can be effectively performed using an appropriate exact simulation method. We examine numerical accuracy and reliability of various types of the saddlepoint approximation techniques when applied to pricing derivatives on discrete realized variance under different types of asset price processes. The limitations of the saddlepoint approximation methods in pricing variance products and volatility derivatives are also discussed. Journal: Applied Mathematical Finance Pages: 1-31 Issue: 1 Volume: 21 Year: 2014 Month: 3 X-DOI: 10.1080/1350486X.2013.780770 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.780770 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:1:p:1-31 Template-Type: ReDIF-Article 1.0 Author-Name: Guanying Wang Author-X-Name-First: Guanying Author-X-Name-Last: Wang Author-Name: Xingchun Wang Author-X-Name-First: Xingchun Author-X-Name-Last: Wang Author-Name: Yongjin Wang Author-X-Name-First: Yongjin Author-X-Name-Last: Wang Title: Rare Shock, Two-Factor Stochastic Volatility and Currency Option Pricing Abstract: In this paper, we develop an option valuation model where the dynamics of the spot foreign exchange rate is governed by a two-factor Markov-modulated jump-diffusion process. The short-term fluctuation of stochastic volatility is driven by a Cox--Ingersoll--Ross (CIR) process and the long-term variation of stochastic volatility is driven by a continuous-time Markov chain which can be interpreted as economy states. Rare events are governed by a compound Poisson process with log-normal jump amplitude and stochastic jump intensity is modulated by a common continuous-time Markov chain. Since the market is incomplete under regime-switching assumptions, we determine a risk-neutral martingale measure via the Esscher transform and then give a pricing formula of currency options. Numerical results are presented for investigating the impact of the long-term volatility and the annual jump intensity on option prices. Journal: Applied Mathematical Finance Pages: 32-50 Issue: 1 Volume: 21 Year: 2014 Month: 3 X-DOI: 10.1080/1350486X.2013.798452 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.798452 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:1:p:32-50 Template-Type: ReDIF-Article 1.0 Author-Name: Jan-Frederik Mai Author-X-Name-First: Jan-Frederik Author-X-Name-Last: Mai Author-Name: Pablo Olivares Author-X-Name-First: Pablo Author-X-Name-Last: Olivares Author-Name: Steffen Schenk Author-X-Name-First: Steffen Author-X-Name-Last: Schenk Author-Name: Matthias Scherer Author-X-Name-First: Matthias Author-X-Name-Last: Scherer Title: A Multivariate Default Model with Spread and Event Risk Abstract: We present a new portfolio default model based on a conditionally independent and identically distributed (CIID) structure of the default times. It combines an intensity-based ansatz in the spirit of Duffie and Gârleanu (2001). Risk and valuation of collateralized debt obligations. Financial Analysts Journal, 57(1), 41--59. with the L�vy subordinator concept introduced in Mai and Scherer (2009). A tractable multivariate default model based on a stochastic time-change. International Journal of Theoretical and Applied Finance, 12(2), 227--249. We aim at exploiting the computational advantages of the CIID framework for evaluating multiname credit derivatives, while incorporating two central drivers for credit products. More precisely, we allow for both a dynamic evolution of the portfolio credit default swap (CDS) spread (unlike static copula models) and cataclysmic events allowing for simultaneous defaults (unlike intensity-based portfolio loss processes). While the former feature is considered to be crucial for consistently hedging credit products, the second property is supposed to take into account default clusters and the market's fear of extreme events. For applications, the model is approximated by a related top-down representation of the portfolio loss process. It is shown how to coherently calculate hedging deltas for collateralized debt obligations (CDOs) w.r.t. portfolio CDS and how to consistently calibrate the model to the two products. Both tasks solely require the computation of one-dimensional (Laplace inversion) integrals and can be carried out within fractions of a second. Illustrating the stability and functionality of the pricing approach, the new model and the models it is related to are calibrated to a daily time-series of iTraxx Europe index CDS and CDOs. We find the fitting results of the presented model to be very promising and conclude that it may be used for the dynamic pricing and hedging of credit derivatives. Journal: Applied Mathematical Finance Pages: 51-83 Issue: 1 Volume: 21 Year: 2014 Month: 3 X-DOI: 10.1080/1350486X.2013.803705 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.803705 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:1:p:51-83 Template-Type: ReDIF-Article 1.0 Author-Name: S. M. Ould Aly Author-X-Name-First: S. M. Author-X-Name-Last: Ould Aly Title: Forward Variance Dynamics: Bergomi's Model Revisited Abstract: In this article, we propose an arbitrage-free modelling framework for the joint dynamics of forward variance along with the underlying index, which can be seen as a combination of the two approaches proposed by Bergomi. The difference between our modelling framework and the Bergomi (2008. Smile dynamics III. Risk, October, 90--96) models is mainly the ability to compute the prices of VIX futures and options by using semi-analytic formulas. Also, we can express the sensitivities of the prices of VIX futures and options with respect to the model parameters, which enables us to propose an efficient and easy calibration to the VIX futures and options. The calibrated model allows to Delta-hedge VIX options by trading in VIX futures, the corresponding hedge ratios can be computed analytically. Journal: Applied Mathematical Finance Pages: 84-107 Issue: 1 Volume: 21 Year: 2014 Month: 3 X-DOI: 10.1080/1350486X.2013.812329 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.812329 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:1:p:84-107 Template-Type: ReDIF-Article 1.0 Author-Name: Hideharu Funahashi Author-X-Name-First: Hideharu Author-X-Name-Last: Funahashi Author-Name: Masaaki Kijima Author-X-Name-First: Masaaki Author-X-Name-Last: Kijima Title: An Extension of the Chaos Expansion Approximation for the Pricing of Exotic Basket Options Abstract: Funahashi and Kijima (in press, A chaos expansion approach for the pricing of contingent claims, Journal of Computational Finance) have proposed an approximation method based on the Wiener--Ito chaos expansion for the pricing of European-style contingent claims. In this paper, we extend the method to the multi-asset case with general local volatility structure for the pricing of exotic basket options such as Asian basket options. Through ample numerical experiments, we show that the accuracy of our approximation remains quite high even for a complex basket option with long maturity and high volatility. Journal: Applied Mathematical Finance Pages: 109-139 Issue: 2 Volume: 21 Year: 2014 Month: 4 X-DOI: 10.1080/1350486X.2013.812855 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.812855 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:2:p:109-139 Template-Type: ReDIF-Article 1.0 Author-Name: Carole Bernard Author-X-Name-First: Carole Author-X-Name-Last: Bernard Author-Name: Zhenyu Cui Author-X-Name-First: Zhenyu Author-X-Name-Last: Cui Title: Prices and Asymptotics for Discrete Variance Swaps Abstract: We study the fair strike of a discrete variance swap for a general time-homogeneous stochastic volatility model. In the special cases of Heston, Hull--White and Sch�bel--Zhu stochastic volatility models, we give simple explicit expressions (improving Broadie and Jain (2008a). The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761--797) in the case of the Heston model). We give conditions on parameters under which the fair strike of a discrete variance swap is higher or lower than that of the continuous variance swap. The interest rate and the correlation between the underlying price and its volatility are key elements in this analysis. We derive asymptotics for the discrete variance swaps and compare our results with those of Broadie and Jain (2008a. The effect of jumps and discrete sampling on volatility and variance swaps. International Journal of Theoretical and Applied Finance, 11(8), 761--797), Jarrow et al. (2013. Discretely sampled variance and volatility swaps versus their continuous approximations. Finance and Stochastics, 17(2), 305--324) and Keller-Ressel and Griessler (2012. Convex order of discrete, continuous and predictable quadratic variation and applications to options on variance. Working paper. Retrieved from http://arxiv.org/abs/1103.2310. Journal: Applied Mathematical Finance Pages: 140-173 Issue: 2 Volume: 21 Year: 2014 Month: 4 X-DOI: 10.1080/1350486X.2013.820524 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.820524 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:2:p:140-173 Template-Type: ReDIF-Article 1.0 Author-Name: Peter W. Duck Author-X-Name-First: Peter W. Author-X-Name-Last: Duck Author-Name: Geoffrey W. Evatt Author-X-Name-First: Geoffrey W. Author-X-Name-Last: Evatt Author-Name: Paul V. Johnson Author-X-Name-First: Paul V. Author-X-Name-Last: Johnson Title: Perpetual Options on Multiple Underlyings Abstract: We study three classes of perpetual option with multiple uncertainties and American-style exercise boundaries, using a partial differential equation-based approach. A combination of accurate numerical techniques and asymptotic analyses is implemented, with each approach informing and confirming the other. The first two examples we study are a put basket option and a call basket option, both involving two stochastic underlying assets, whilst the third is a (novel) class of real option linked to stochastic demand and costs (the details of the modelling for this are described in the paper). The Appendix addresses the issue of pricing American-style perpetual options involving (just) one stochastic underlying, but in which the volatility is also modelled stochastically, using the Heston (1993) framework. Journal: Applied Mathematical Finance Pages: 174-200 Issue: 2 Volume: 21 Year: 2014 Month: 4 X-DOI: 10.1080/1350486X.2013.825437 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.825437 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:2:p:174-200 Template-Type: ReDIF-Article 1.0 Author-Name: Aurélien Alfonsi Author-X-Name-First: Aurélien Author-X-Name-Last: Alfonsi Author-Name: José Infante Acevedo Author-X-Name-First: José Infante Author-X-Name-Last: Acevedo Title: Optimal Execution and Price Manipulations in Time-varying Limit Order Books Abstract: This paper focuses on an extension of the limit order book (LOB) model with general shape introduced by Alfonsi, Fruth and Schied ((2010). Optimal execution strategies in limit order books with general shape functions. Quantitative Finance, 10(2), 143-157). Here, the additional feature allows a time-varying LOB depth. We solve the optimal execution problem in this framework for both discrete and continuous time strategies. This gives in particular sufficient conditions to exclude price manipulations in the sense of Huberman and Stanzl ((2004). Price manipulation and quasi-arbitrage. Econometrica, 72(4), 1247-1275) or transaction-triggered price manipulations (see Alfonsi, A., Schied, A., & Slynko, A. (2012). Order book resilience, prince manipulation, and the positive portfolio problem. SIAM Journal of Financial Mathematics, 3, 511-533.). These conditions give interesting qualitative insights on how market makers may create or not price manipulations. Journal: Applied Mathematical Finance Pages: 201-237 Issue: 3 Volume: 21 Year: 2014 Month: 7 X-DOI: 10.1080/1350486X.2013.845471 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.845471 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:3:p:201-237 Template-Type: ReDIF-Article 1.0 Author-Name: Raymond Brummelhuis Author-X-Name-First: Raymond Author-X-Name-Last: Brummelhuis Author-Name: Ron T. L. Chan Author-X-Name-First: Ron T. L. Author-X-Name-Last: Chan Title: A Radial Basis Function Scheme for Option Pricing in Exponential Lévy Models Abstract: We use Radial Basis Function (RBF) interpolation to price options in exponential Lévy models by numerically solving the fundamental pricing PIDE (Partial integro-differential equations). Our RBF scheme can handle arbitrary singularities of the Lévy measure in 0 without introducing further approximations, making it simpler to implement than competing methods. In numerical experiments using processes from the CGMY-KoBoL class, the scheme is found to be second order convergent in the number of interpolation points, including for processes of unbounded variation. Journal: Applied Mathematical Finance Pages: 238-269 Issue: 3 Volume: 21 Year: 2014 Month: 7 X-DOI: 10.1080/1350486X.2013.850902 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.850902 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:3:p:238-269 Template-Type: ReDIF-Article 1.0 Author-Name: Yuta Katsuki Author-X-Name-First: Yuta Author-X-Name-Last: Katsuki Author-Name: Koichi Matsumoto Author-X-Name-First: Koichi Author-X-Name-Last: Matsumoto Title: Tail VaR Measures in a Multi-period Setting Abstract: This paper studies a coherent acceptability measure which is a negative coherent risk measure, in a multi-period model. When a coherent acceptability measure changes according to new information in the market, a time consistency plays an important role. The usual strong time consistency gives too severe a multi-period Tail Value at Risk (Tail VaR) from a practical viewpoint. We study a weak type of time consistency and propose new multi-period Tail VaR measures. Journal: Applied Mathematical Finance Pages: 270-297 Issue: 3 Volume: 21 Year: 2014 Month: 7 X-DOI: 10.1080/1350486X.2013.851449 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.851449 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:3:p:270-297 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Baldeaux Author-X-Name-First: Jan Author-X-Name-Last: Baldeaux Author-Name: Alexander Badran Author-X-Name-First: Alexander Author-X-Name-Last: Badran Title: Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model Abstract: The paper demonstrates that a pure-diffusion 3/2 model is able to capture the observed upward-sloping implied volatility skew in VIX options. This observation contradicts a common perception in the literature that jumps are required for the consistent modelling of equity and VIX derivatives. The pure-diffusion model, however, struggles to reproduce the smile in the implied volatilities of short-term index options. The pronounced implied volatility smile produces artificially inflated fitted parameters, resulting in unrealistically high VIX option implied volatilities. To remedy these shortcomings, jumps are introduced. The resulting model is able to better fit short-term index option implied volatilities while producing more realistic VIX option implied volatilities, without a loss in tractability. Journal: Applied Mathematical Finance Pages: 299-312 Issue: 4 Volume: 21 Year: 2014 Month: 9 X-DOI: 10.1080/1350486X.2013.868631 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.868631 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:4:p:299-312 Template-Type: ReDIF-Article 1.0 Author-Name: Emmanuel Lépinette Author-X-Name-First: Emmanuel Author-X-Name-Last: Lépinette Author-Name: Tuan Tran Author-X-Name-First: Tuan Author-X-Name-Last: Tran Title: Approximate Hedging in a Local Volatility Model with Proportional Transaction Costs Abstract: A<sc>bstract</sc>Local volatility models are popular as they can be calibrated to the market of European options by the simple Dupire formula. For such a model, we propose a modified Leland method which allows to approximately replicate a European contingent claim when the market is under proportional transaction costs. The convergence of the scheme is shown by means of a new strategy of proof based on partial differential equations (PDEs) techniques allowing us to obtain appropriate Greek estimations. Journal: Applied Mathematical Finance Pages: 313-341 Issue: 4 Volume: 21 Year: 2014 Month: 9 X-DOI: 10.1080/1350486X.2013.871802 File-URL: http://hdl.handle.net/10.1080/1350486X.2013.871802 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:4:p:313-341 Template-Type: ReDIF-Article 1.0 Author-Name: Patrick Cheridito Author-X-Name-First: Patrick Author-X-Name-Last: Cheridito Author-Name: Tardu Sepin Author-X-Name-First: Tardu Author-X-Name-Last: Sepin Title: Optimal Trade Execution Under Stochastic Volatility and Liquidity Abstract: We study the problem of optimally liquidating a financial position in a discrete-time model with stochastic volatility and liquidity. We consider the three cases where the objective is to minimize the expectation, an expected exponential or a mean-variance criterion of the implementation cost. In the first case, the optimal solution can be fully characterized by a forward-backward system of stochastic equations depending on conditional expectations of future liquidity. In the other two cases, we derive Bellman equations from which the optimal solutions can be obtained numerically by discretizing the control space. In all three cases, we compute optimal strategies for different simulated realizations of prices, volatility and liquidity and compare the outcomes to the ones produced by the deterministic strategies of Bertsimas and Lo (1998; Optimal control of execution costs. Journal of Financial Markets, 1, 1-50) and Almgren and Chriss (2001; Optimal execution of portfolio transactions. Journal of Risk, 3, 5-33). Journal: Applied Mathematical Finance Pages: 342-362 Issue: 4 Volume: 21 Year: 2014 Month: 9 X-DOI: 10.1080/1350486X.2014.881005 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.881005 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:4:p:342-362 Template-Type: ReDIF-Article 1.0 Author-Name: Barbara G�tz Author-X-Name-First: Barbara Author-X-Name-Last: G�tz Author-Name: Marcos Escobar Author-X-Name-First: Marcos Author-X-Name-Last: Escobar Author-Name: Rudi Zagst Author-X-Name-First: Rudi Author-X-Name-Last: Zagst Title: Closed-Form Pricing of Two-Asset Barrier Options with Stochastic Covariance Abstract: Single and double barrier options on more than one underlying with stochastic volatility are usually priced via Monte Carlo simulation due to the non-existence of closed-form solutions for their value. In this paper, for a special dependence structure, the prices of some two-asset barrier derivatives, like double-digital options and correlation options can be derived analytically using generalized Fourier transforms and some conditions on the characteristic functions. We study the influence of the various parameters on these prices and show that these formulas can be easily and quickly computed. We also extend our approach to further allow for a random correlation structure. Journal: Applied Mathematical Finance Pages: 363-397 Issue: 4 Volume: 21 Year: 2014 Month: 9 X-DOI: 10.1080/1350486X.2014.881662 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.881662 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:4:p:363-397 Template-Type: ReDIF-Article 1.0 Author-Name: Indranil SenGupta Author-X-Name-First: Indranil Author-X-Name-Last: SenGupta Title: Option Pricing with Transaction Costs and Stochastic Interest Rate Abstract: In the case when transaction costs are associated with trading assets the option pricing problem is known to lead to solving nonlinear partial differential equations even when the underlying asset is modelled using a simple geometric Brownian motion. The nonlinear term in the resulting PDE corresponds to the presence of transaction costs. We generalize this model to a stochastic one-factor interest rate model. We show that the model follows a nonlinear parabolic type partial differential equation. Under certain assumption we prove the existence of classical solution for this model. Journal: Applied Mathematical Finance Pages: 399-416 Issue: 5 Volume: 21 Year: 2014 Month: 11 X-DOI: 10.1080/1350486X.2014.881263 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.881263 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:5:p:399-416 Template-Type: ReDIF-Article 1.0 Author-Name: Ernst Eberlein Author-X-Name-First: Ernst Author-X-Name-Last: Eberlein Author-Name: Kathrin Glau Author-X-Name-First: Kathrin Author-X-Name-Last: Glau Title: Variational Solutions of the Pricing PIDEs for European Options in Lévy Models Abstract: One of the fundamental problems in financial mathematics is to develop efficient algorithms for pricing options in advanced models such as those driven by Lévy processes. Essentially there are three approaches in use. These are Monte Carlo, Fourier transform and partial integro-differential equation (PIDE)-based methods. We focus our attention here on the latter. There is a large arsenal of numerical methods for efficiently solving parabolic equations that arise in this context. Especially Galerkin and Galerkin-inspired methods have an impressive potential. In order to apply these methods, what is required is a formulation of the equation in the weak sense.The contribution of this paper is therefore to analyse weak solutions of the Kolmogorov backward equations which are related to prices of European options in (time-inhomogeneous) Lévy models and to establish a precise link between the prices and the weak solutions of these equations. The resulting relation is a Feynman-Kac representation of the solution as a conditional expectation. Our special concern is to provide a framework that is able to cover both, the common types of European options and a wide range of advanced models in which these derivatives are priced.An application to financial models requires in particular to admit pure jump processes such as generalized hyperbolic processes as well as unbounded domains of the equation. In order to deal at the same time with the typical pay-offs that can arise, the weak formulation of the equation is based on exponentially weighted Sobolev-Slobodeckii spaces. We provide a number of examples of models that are covered by this general framework. Examples of options for which such an analysis is required are calls, puts, digital and power options as well as basket options. Journal: Applied Mathematical Finance Pages: 417-450 Issue: 5 Volume: 21 Year: 2014 Month: 11 X-DOI: 10.1080/1350486X.2014.886817 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.886817 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:5:p:417-450 Template-Type: ReDIF-Article 1.0 Author-Name: Joanne E. Kennedy Author-X-Name-First: Joanne E. Author-X-Name-Last: Kennedy Author-Name: Duy Pham Author-X-Name-First: Duy Author-X-Name-Last: Pham Title: On the Approximation of the SABR with Mean Reversion Model: A Probabilistic Approach Abstract: In this paper, we study the stochastic alpha beta rho with mean reversion model (SABR-MR). We first compare the SABR model with the SABR-MR model in terms of future volatility to point out the fundamental difference in the models' dynamics. We then derive an efficient probabilistic approximation for the SABR-MR model to price European options. Similar to the method derived in Kennedy, J. E., Mitra, S., & Pham, D. (2012). On the approximation of the SABR model: A probabilistic approach. Applied Mathematical Finance, 19(6), 553-586., we focus on capturing the terminal distribution of the underlying asset (conditional on the terminal volatility) to arrive at the implied volatilities of the corresponding European options for all strikes and maturities. Our resulting method allows us to work with a wide range of parameters that cover the long-dated option and different market conditions. Journal: Applied Mathematical Finance Pages: 451-481 Issue: 5 Volume: 21 Year: 2014 Month: 11 X-DOI: 10.1080/1350486X.2014.888146 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.888146 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:5:p:451-481 Template-Type: ReDIF-Article 1.0 Author-Name: Carlos Fuertes Author-X-Name-First: Carlos Author-X-Name-Last: Fuertes Author-Name: Andrew Papanicolaou Author-X-Name-First: Andrew Author-X-Name-Last: Papanicolaou Title: Implied Filtering Densities on the Hidden State of Stochastic Volatility Abstract: We formulate and analyse an inverse problem using derivative prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional expectations that are already observed in the market, and which can be used as input to an inverse problem whose solution is an implied conditional density on volatility. Our analysis relies on a specification of the martingale change of measure, which we refer to as separability. This specification has a multiplicative component that behaves like a risk premium on volatility uncertainty in the market. When applied to SPX options data, the estimated model and implied densities produce variance-swap rates that are consistent with the VIX volatility index. The implied densities are relatively stable over time and pick up some of the monthly effects that occur due to the options' expiration, indicating that the volatility-uncertainty premium could experience cyclic effects due to the maturity date of the options. Journal: Applied Mathematical Finance Pages: 483-522 Issue: 6 Volume: 21 Year: 2014 Month: 12 X-DOI: 10.1080/1350486X.2014.891357 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.891357 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:6:p:483-522 Template-Type: ReDIF-Article 1.0 Author-Name: Ting Ting Huang Author-X-Name-First: Ting Ting Author-X-Name-Last: Huang Author-Name: Bruce Qiang Sun Author-X-Name-First: Bruce Qiang Author-X-Name-Last: Sun Author-Name: Xinfu Chen Author-X-Name-First: Xinfu Author-X-Name-Last: Chen Title: Re-specification of Affine Term Structure Models: The Linkage to Empirical Investigations Abstract: This paper specifies the dynamic and cross-sectional behaviour of bonds in the framework of the general affine term structure model (ATSM) of Duffie and Kan (1996, A yield-factor model of interest rate. Mathematical Finance, 6, 379-406). We present the calibrations of ATSM, with the numerics fitting in with the actual data under the physical probability measure. Without assumptions and restrictions on any specific physical process of the factors, we find theoretical loads by solving Riccati equations with parameters chosen for the solution to match those from the principal component models. The general condition on the boundary is satisfied; so, the Black-Scholes equation admits a unique solution, which supports the Condition of Duffie and Kan. Journal: Applied Mathematical Finance Pages: 523-554 Issue: 6 Volume: 21 Year: 2014 Month: 12 X-DOI: 10.1080/1350486X.2014.896510 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.896510 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:6:p:523-554 Template-Type: ReDIF-Article 1.0 Author-Name: Marcos Escobar Author-X-Name-First: Marcos Author-X-Name-Last: Escobar Author-Name: Barbara G�tz Author-X-Name-First: Barbara Author-X-Name-Last: G�tz Author-Name: Daniela Neykova Author-X-Name-First: Daniela Author-X-Name-Last: Neykova Author-Name: Rudi Zagst Author-X-Name-First: Rudi Author-X-Name-Last: Zagst Title: Stochastic Correlation and Volatility Mean-reversion - Empirical Motivation and Derivatives Pricing via Perturbation Theory Abstract: The dependence structure is crucial when modelling several assets simultaneously. We show for a real-data example that the correlation structure between assets is not constant over time but rather changes stochastically, and we propose a multidimensional asset model which fits the patterns found in the empirical data. The model is applied to price multi-asset derivatives by means of perturbation theory. It turns out that the leading term of the approximation corresponds to the Black-Scholes derivative price with correction terms adjusting for stochastic volatility and stochastic correlation effects. The practicability of the presented method is illustrated by some numerical implementations. Furthermore, we propose a calibration methodology for the considered model. Journal: Applied Mathematical Finance Pages: 555-594 Issue: 6 Volume: 21 Year: 2014 Month: 12 X-DOI: 10.1080/1350486X.2014.906972 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.906972 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:6:p:555-594 Template-Type: ReDIF-Article 1.0 Author-Name: Sai Hung Marten Ting Author-X-Name-First: Sai Hung Marten Author-X-Name-Last: Ting Author-Name: Christian-Oliver Ewald Author-X-Name-First: Christian-Oliver Author-X-Name-Last: Ewald Title: Asymptotic Solutions for Australian Options with Low Volatility Abstract: In this paper we derive asymptotic expansions for Australian options in the case of low volatility using the method of matched asymptotics. The expansion is performed on a volatility scaled parameter. We obtain a solution that is of up to the third order. In case that there is no drift in the underlying, the solution provided is in closed form, for a non-zero drift, all except one of the components of the solutions are in closed form. Additionally, we show that in some non-zero drift cases, the solution can be further simplified and in fact written in closed form as well. Numerical experiments show that the asymptotic solutions derived here are quite accurate for low volatility. Journal: Applied Mathematical Finance Pages: 595-613 Issue: 6 Volume: 21 Year: 2014 Month: 12 X-DOI: 10.1080/1350486X.2014.906973 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.906973 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:21:y:2014:i:6:p:595-613 Template-Type: ReDIF-Article 1.0 Author-Name: Rehez Ahlip Author-X-Name-First: Rehez Author-X-Name-Last: Ahlip Author-Name: Marek Rutkowski Author-X-Name-First: Marek Author-X-Name-Last: Rutkowski Title: Semi-analytical Pricing of Currency Options in the Heston/CIR Jump-Diffusion Hybrid Model Abstract: We examine currency options in the jump-diffusion version of the Heston stochastic volatility model for the exchange rate. We assume, in addition, that the domestic and foreign stochastic interest rates are governed by the CIR dynamics. The instantaneous volatility is correlated with the dynamics of the exchange rate return, whereas the domestic and foreign short-term rates are assumed to be independent of the dynamics of the exchange rate and its volatility. The main result furnishes a semi-analytical formula for the price of the European currency call option in the hybrid foreign exchange/interest rates model. Journal: Applied Mathematical Finance Pages: 1-27 Issue: 1 Volume: 22 Year: 2015 Month: 3 X-DOI: 10.1080/1350486X.2014.928227 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.928227 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:1:p:1-27 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Author-Name: Giulia Di Nunno Author-X-Name-First: Giulia Author-X-Name-Last: Di Nunno Author-Name: Asma Khedher Author-X-Name-First: Asma Author-X-Name-Last: Khedher Author-Name: Maren Diane Schmeck Author-X-Name-First: Maren Diane Author-X-Name-Last: Schmeck Title: Pricing of Spread Options on a Bivariate Jump Market and Stability to Model Risk Abstract: We study the pricing of spread options and we obtain a Margrabe-type formula for a bivariate jump-diffusion model. Moreover, we study the robustness of the price to model risk, in the sense that we consider two types of bivariate jump-diffusion models: one allowing for infinite activity small jumps and one not. In the second model, an adequate continuous component describes the small variation of prices. We illustrate our computations by several examples. Journal: Applied Mathematical Finance Pages: 28-62 Issue: 1 Volume: 22 Year: 2015 Month: 3 X-DOI: 10.1080/1350486X.2014.948708 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.948708 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:1:p:28-62 Template-Type: ReDIF-Article 1.0 Author-Name: Rohini Kumar Author-X-Name-First: Rohini Author-X-Name-Last: Kumar Title: Effect of Volatility Clustering on Indifference Pricing of Options by Convex Risk Measures Abstract: In this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indifference price in their article is obtained by using dynamic convex risk measures given by backward stochastic differential equations. Volatility clustering is modelled by a fast mean-reverting volatility in a stochastic volatility model for stock price. Asymptotics of the indifference price of options and their corresponding implied volatility are obtained in this article, as the mean-reversion time approaches zero. Correction terms to the asymptotic option price and implied volatility are also obtained. Journal: Applied Mathematical Finance Pages: 63-82 Issue: 1 Volume: 22 Year: 2015 Month: 3 X-DOI: 10.1080/1350486X.2014.949805 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.949805 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:1:p:63-82 Template-Type: ReDIF-Article 1.0 Author-Name: Ralf Korn Author-X-Name-First: Ralf Author-X-Name-Last: Korn Author-Name: Mykhailo Pupashenko Author-X-Name-First: Mykhailo Author-X-Name-Last: Pupashenko Title: A New Variance Reduction Technique for Estimating Value-at-Risk Abstract: In this article we present a new variance reduction technique for estimating the Value-at-Risk (VaR) of a portfolio of various securities via Monte Carlo (MC) simulation. The technique can be applied for any type of distribution of the risk factors, no matter if light- or heavy-tailed. It consists of a particular variant of importance sampling where the change of measure is obtained by using an approximation to an optimal importance sampling density. Any approximation of the portfolio loss function (such as the popular Delta-Gamma approximation) can be used. An in-depth numerical study in the case of risk factors with light-tailed distributions exhibits a great variance reduction when estimating the probability of large portfolio losses outperforming other known methods. Journal: Applied Mathematical Finance Pages: 83-98 Issue: 1 Volume: 22 Year: 2015 Month: 3 X-DOI: 10.1080/1350486X.2014.962182 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.962182 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:1:p:83-98 Template-Type: ReDIF-Article 1.0 Author-Name: Ruggero Caldana Author-X-Name-First: Ruggero Author-X-Name-Last: Caldana Author-Name: Gerald H. L. Cheang Author-X-Name-First: Gerald H. L. Author-X-Name-Last: Cheang Author-Name: Carl Chiarella Author-X-Name-First: Carl Author-X-Name-Last: Chiarella Author-Name: Gianluca Fusai Author-X-Name-First: Gianluca Author-X-Name-Last: Fusai Title: Correction: Exchange Option under Jump-diffusion Dynamics Abstract: In this note, we provide the correct formula for the price of the European exchange option given in Cheang, G. H. L., & Chiarella, C. (2011. Exchange options under jump-diffusion dynamics. Applied Mathematical Finance, 18, 245-276) in a bi-dimensional jump diffusion model. Journal: Applied Mathematical Finance Pages: 99-103 Issue: 1 Volume: 22 Year: 2015 Month: 3 X-DOI: 10.1080/1350486X.2014.937564 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.937564 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:1:p:99-103 Template-Type: ReDIF-Article 1.0 Author-Name: Roberto Baviera Author-X-Name-First: Roberto Author-X-Name-Last: Baviera Author-Name: Alessandro Cassaro Author-X-Name-First: Alessandro Author-X-Name-Last: Cassaro Title: A Note on Dual-Curve Construction: Mr. Crab's Bootstrap Abstract: Observe crabs in the sand of our beaches: they move forward, backward and then forward again. Before the crisis, the standard bootstrap of interest rate curves was a 'Forward'-looking iterative algorithm where only information from previous knots was used to find discounts at subsequent dates.In this note we describe a new bootstrapping technique that involves various 'Backward' steps, which are reminiscent of a crab's steps: this new methodology coherently considers now standard dual-curve framework. Two other major results emerge from the bootstrap methodology described: (i) discounts are independent from the chosen interpolation rule for all practical purposes; and (ii) convexity adjustments to Short-Term Interest Rate futures can be dealt with using a methodology in line with market practice. Journal: Applied Mathematical Finance Pages: 105-132 Issue: 2 Volume: 22 Year: 2015 Month: 4 X-DOI: 10.1080/1350486X.2014.959665 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.959665 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:2:p:105-132 Template-Type: ReDIF-Article 1.0 Author-Name: Yuji Umezawa Author-X-Name-First: Yuji Author-X-Name-Last: Umezawa Author-Name: Akira Yamazaki Author-X-Name-First: Akira Author-X-Name-Last: Yamazaki Title: Pricing Path-Dependent Options with Discrete Monitoring under Time-Changed Lévy Processes Abstract: This paper proposes a pricing method for path-dependent derivatives with discrete monitoring when an underlying asset price is driven by a time-changed Lévy process. The key to our method is to derive a backward recurrence relation for computing the multivariate characteristic function of the intertemporal joint distribution of the time-changed Lévy process. Using the derived representation of the characteristic function, we obtain semi-analytical pricing formulas for geometric Asian, forward start, barrier, fader and lookback options, all of which are discretely monitored. Journal: Applied Mathematical Finance Pages: 133-161 Issue: 2 Volume: 22 Year: 2015 Month: 4 X-DOI: 10.1080/1350486X.2014.960529 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.960529 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:2:p:133-161 Template-Type: ReDIF-Article 1.0 Author-Name: Tim Leung Author-X-Name-First: Tim Author-X-Name-Last: Leung Author-Name: Ronnie Sircar Author-X-Name-First: Ronnie Author-X-Name-Last: Sircar Title: Implied Volatility of Leveraged ETF Options Abstract: This paper studies the problem of understanding implied volatilities from options written on leveraged exchanged-traded funds (LETFs), with an emphasis on the relations between LETF options with different leverage ratios. We first examine from empirical data the implied volatility skews for LETF options based on the S&P 500. In order to enhance their comparison with non-leveraged ETFs, we introduce the concept of moneyness scaling and provide a new formula that links option implied volatilities between leveraged and unleveraged ETFs. Under a multiscale stochastic volatility framework, we apply asymptotic techniques to derive an approximation for both the LETF option price and implied volatility. The approximation formula reflects the role of the leverage ratio, and thus allows us to link implied volatilities of options on an ETF and its leveraged counterparts. We apply our result to quantify matches and mismatches in the level and slope of the implied volatility skews for various LETF options using data from the underlying ETF option prices. This reveals some apparent biases in the leverage implied by the market prices of different products, long and short with leverage ratios two times and three times. Journal: Applied Mathematical Finance Pages: 162-188 Issue: 2 Volume: 22 Year: 2015 Month: 4 X-DOI: 10.1080/1350486X.2014.975825 File-URL: http://hdl.handle.net/10.1080/1350486X.2014.975825 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:2:p:162-188 Template-Type: ReDIF-Article 1.0 Author-Name: Mohammed A. Aba Oud Author-X-Name-First: Mohammed A. Author-X-Name-Last: Aba Oud Author-Name: Joanna Goard Author-X-Name-First: Joanna Author-X-Name-Last: Goard Title: Stochastic Models for Oil Prices and the Pricing of Futures on Oil Abstract: In this article, we investigate and compare the performance of various one-factor diffusion models in their ability to capture the behaviour of Brent crude oil prices. New proposed models, which have a three-quarters power in the diffusion term, are found to outperform all other popular models tested. Analytic solutions for futures prices under the new models are found and used to calibrate market prices. Results from the calibration show that one of the new three-quarters models with a mean-reverting property outperforms other popular models in fitting and forecasting futures prices. Journal: Applied Mathematical Finance Pages: 189-206 Issue: 2 Volume: 22 Year: 2015 Month: 4 X-DOI: 10.1080/1350486X.2015.1005281 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1005281 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:2:p:189-206 Template-Type: ReDIF-Article 1.0 Author-Name: Tinne Haentjens Author-X-Name-First: Tinne Author-X-Name-Last: Haentjens Author-Name: Karel J. in 't Hout Author-X-Name-First: Karel J. Author-X-Name-Last: in 't Hout Title: ADI Schemes for Pricing American Options under the Heston Model Abstract: In this article, a simple, effective adaptation of Alternating Direction Implicit time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential complementarity problem. The stability and convergence of the new methods are extensively investigated in actual, challenging applications. In addition, a relevant theoretical result is proved. Journal: Applied Mathematical Finance Pages: 207-237 Issue: 3 Volume: 22 Year: 2015 Month: 7 X-DOI: 10.1080/1350486X.2015.1009129 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1009129 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:3:p:207-237 Template-Type: ReDIF-Article 1.0 Author-Name: Yerkin Kitapbayev Author-X-Name-First: Yerkin Author-X-Name-Last: Kitapbayev Title: The British Lookback Option with Fixed Strike Abstract: We continue research of the new type of options called 'British' that was introduced recently by presenting the British lookback option with fixed strike. This article generalizes the work about the British Russian option and provides financial analysis of lookback options with fixed non-zero strike. The British holder enjoys the early exercise feature of American options whereupon his pay-off (deliverable immediately) is the 'best prediction' of the European lookback pay-off under the hypothesis that the true drift of the stock price equals a contract drift. We derive a closed-form expression for the arbitrage-free price in terms of the optimal stopping boundary of two-dimensional optimal stopping problem with a scaling strike and show that the rational exercise boundary of the option can be characterized via the unique solution to a nonlinear integral equation. We also show the remarkable numerical example where the rational exercise boundary exhibits a discontinuity. Using these results, we perform a financial analysis of the British lookback option with fixed strike, which shows that with the contract drift properly selected this instrument not only provides an effective protection mechanism, but becomes a very attractive alternative to the classic European/American lookback option from speculator's point of view and gives high returns when stock movements are favourable. Journal: Applied Mathematical Finance Pages: 238-260 Issue: 3 Volume: 22 Year: 2015 Month: 7 X-DOI: 10.1080/1350486X.2015.1019156 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1019156 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:3:p:238-260 Template-Type: ReDIF-Article 1.0 Author-Name: Pietro Fodra Author-X-Name-First: Pietro Author-X-Name-Last: Fodra Author-Name: Huyên Pham Author-X-Name-First: Huyên Author-X-Name-Last: Pham Title: Semi-Markov Model for Market Microstructure Abstract: We introduce a new model based on Markov renewal processes (MRP) describing the fluctuations of a tick-by-tick single asset price. We consider a point process associated to the timestamps of the price jumps, with marks associated to price increments. By modelling the marks with a suitable Markov chain, we can reproduce the strong mean-reversion of price returns, a phenomenon known as microstructure noise. Moreover, using MRP, we can model the alternating of time intervals with high and low market activity, and consider dependence between price increments and jump times. We also provide simple parametric and nonparametric statistical procedures for the estimation of our model. We obtain closed-form formula for the mean signature plot, and show the diffusive behaviour of our model at large-scale limit. We illustrate our results by numerical simulations, and find that our model is consistent with available empirical data. Journal: Applied Mathematical Finance Pages: 261-295 Issue: 3 Volume: 22 Year: 2015 Month: 7 X-DOI: 10.1080/1350486X.2015.1037963 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1037963 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:3:p:261-295 Template-Type: ReDIF-Article 1.0 Author-Name: Leung Author-X-Name-First: Author-X-Name-Last: Leung Author-Name: Nan Chen Author-X-Name-First: Nan Author-X-Name-Last: Chen Author-Name: Kwok Author-X-Name-First: Author-X-Name-Last: Kwok Title: Game Options Analysis of the Information Role of Call Policies in Convertible Bonds Abstract: In debt financing, existence of information asymmetry on the firm quality between the firm management and bond investors may lead to significant adverse selection costs. We develop the two-stage sequential dynamic two-person game option models to analyse the market signalling role of the callable feature in convertible bonds. We show that firms with positive private information on earning potential may signal their type to investors via the callable feature in a convertible bond. We present the variational inequalities formulation with respect to various equilibrium strategies in the two-person game option models via characterization of the optimal stopping rules adopted by the bond issuer and bondholders. The bondholders' belief system on the firm quality may be revealed with the passage of time when the issuer follows his optimal strategy of declaring call or bankruptcy. Under separating equilibrium, the quality status of the firm is revealed so the information asymmetry game becomes a new game under complete information. To analyse pooling equilibrium, the corresponding incentive compatibility constraint is derived. We manage to deduce the sufficient conditions for the existence of signalling equilibrium of our game option model under information asymmetry. We analyse how the callable feature may lower the adverse selection costs in convertible bond financing. We show how a low-quality firm may benefit from information asymmetry and vice versa, underpricing of the value of debt issued by a high-quality firm. Journal: Applied Mathematical Finance Pages: 297-335 Issue: 4 Volume: 22 Year: 2015 Month: 9 X-DOI: 10.1080/1350486X.2015.1040522 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1040522 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:4:p:297-335 Template-Type: ReDIF-Article 1.0 Author-Name: Olivier Guéant Author-X-Name-First: Olivier Author-X-Name-Last: Guéant Title: Optimal Execution and Block Trade Pricing: A General Framework Abstract: In this article, we develop a general framework to study optimal execution and to price block trades. We prove existence of optimal liquidation strategies and provide regularity results for optimal strategies under very general hypotheses. We exhibit a Hamiltonian characterization for the optimal strategy that can be used for numerical approximation. We also focus on the important topic of block trade pricing and propose a methodology to give a price to financial (il)liquidity. In particular, we provide a closed-form formula for the price of a block trade when there is no time constraint to liquidate. Journal: Applied Mathematical Finance Pages: 336-365 Issue: 4 Volume: 22 Year: 2015 Month: 9 X-DOI: 10.1080/1350486X.2015.1042188 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1042188 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:4:p:336-365 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Baldeaux Author-X-Name-First: Jan Author-X-Name-Last: Baldeaux Author-Name: Fung Author-X-Name-First: Author-X-Name-Last: Fung Author-Name: Katja Ignatieva Author-X-Name-First: Katja Author-X-Name-Last: Ignatieva Author-Name: Eckhard Platen Author-X-Name-First: Eckhard Author-X-Name-Last: Platen Title: A Hybrid Model for Pricing and Hedging of Long-dated Bonds Abstract: Long-dated fixed income securities play an important role in asset-liability management, in life insurance and in annuity businesses. This paper applies the benchmark approach, where the growth optimal portfolio (GOP) is employed as numéraire together with the real-world probability measure for pricing and hedging of long-dated bonds. It employs a time-dependent constant elasticity of variance model for the discounted GOP and takes stochastic interest rate risk into account. This results in a hybrid framework that models the stochastic dynamics of the GOP and the short rate simultaneously. We estimate and compare a variety of continuous-time models for short-term interest rates using non-parametric kernel-based estimation. The hybrid models remain highly tractable and fit reasonably well the observed dynamics of proxies of the GOP and interest rates. Our results involve closed-form expressions for bond prices and hedge ratios. Across all models under consideration we find that the hybrid model with the 3/2 dynamics for the interest rate provides the best fit to the data with respect to lowest prices and least expensive hedges. Journal: Applied Mathematical Finance Pages: 366-398 Issue: 4 Volume: 22 Year: 2015 Month: 9 X-DOI: 10.1080/1350486X.2015.1050119 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1050119 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:4:p:366-398 Template-Type: ReDIF-Article 1.0 Author-Name: Dorje C. Brody Author-X-Name-First: Dorje C. Author-X-Name-Last: Brody Author-Name: Yan Tai Law Author-X-Name-First: Yan Tai Author-X-Name-Last: Law Title: Pricing of Defaultable Bonds with Random Information Flow Abstract: In the information-based approach to asset pricing, the market filtration is modelled explicitly as a superposition of signals concerning relevant market factors and independent noise. The rate at which the signal is revealed to the market then determines the overall magnitude of asset volatility. By letting this information flow rate random, we obtain an elementary stochastic volatility model within the information-based approach. Such an extension is justified on account of the fact that in real markets information flow rates are rarely measurable. Effects of having a random information flow rate are investigated in detail in the context of a simple model setup. Specifically, the price process of an elementary defaultable bond is derived, and its characteristic behaviours are revealed via simulation studies. The price of a European-style option on the bond is worked out, showing that the model has a sufficient flexibility to fit volatility surface. As an extension of the random information flow model, modelling of price manipulation is considered. A simple model is used to show how the skewness of the manipulated and unmanipulated price processes take opposite signature. Journal: Applied Mathematical Finance Pages: 399-420 Issue: 5 Volume: 22 Year: 2015 Month: 11 X-DOI: 10.1080/1350486X.2015.1050151 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1050151 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:5:p:399-420 Template-Type: ReDIF-Article 1.0 Author-Name: Chi Hung Yuen Author-X-Name-First: Chi Hung Author-X-Name-Last: Yuen Author-Name: Wendong Zheng Author-X-Name-First: Wendong Author-X-Name-Last: Zheng Author-Name: Yue Kuen Kwok Author-X-Name-First: Yue Kuen Author-X-Name-Last: Kwok Title: Pricing Exotic Discrete Variance Swaps under the 3/2-Stochastic Volatility Models Abstract: We consider pricing of various types of exotic discrete variance swaps, like the gamma swaps and corridor variance swaps, under the 3/2-stochastic volatility models (SVMs) with jumps in asset price. The class of SVMs that use a constant-elasticity-of-variance (CEV) process for the instantaneous variance exhibits good analytical tractability only when the CEV parameter takes just a few special values (namely 0, 1/2, 1 and 3/2). The popular Heston model corresponds to the choice of the CEV parameter to be 1/2. However, the stochastic volatility dynamics implied by the Heston model fails to capture some important empirical features of the market data. The choice of 3/2 for the CEV parameter in the SVM shows better agreement with empirical studies while it maintains a good level of analytical tractability. Using the partial integro-differential equation (PIDE) formulation, we manage to derive quasi-closed-form pricing formulas for the fair strike prices of various types of exotic discrete variance swaps with various weight processes and different return specifications under the 3/2-model. Pricing properties of these exotic discrete variance swaps with respect to various model parameters are explored. Journal: Applied Mathematical Finance Pages: 421-449 Issue: 5 Volume: 22 Year: 2015 Month: 11 X-DOI: 10.1080/1350486X.2015.1050525 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1050525 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:5:p:421-449 Template-Type: ReDIF-Article 1.0 Author-Name: Gerald H. L. Cheang Author-X-Name-First: Gerald H. L. Author-X-Name-Last: Cheang Author-Name: Guanghua Lian Author-X-Name-First: Guanghua Author-X-Name-Last: Lian Title: Perpetual Exchange Options under Jump-Diffusion Dynamics Abstract: This paper provides a pricing formula for perpetual exchange options, where the dynamics of the underlying assets are driven by jump-diffusion processes. It is an extension of Gerber and Shiu, and also Wong, who have priced perpetual exchange options under the pure-diffusion setting, and that of Gerber and Shiu, who have also considered perpetual options on single assets under jump-diffusion dynamics. It complements the results of Cheang and Chiarella, who derive a probabilistic representation of the American exchange option price under jump-diffusion dynamics. Journal: Applied Mathematical Finance Pages: 450-462 Issue: 5 Volume: 22 Year: 2015 Month: 11 X-DOI: 10.1080/1350486X.2015.1061443 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1061443 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:5:p:450-462 Template-Type: ReDIF-Article 1.0 Author-Name: Gilles Pagès Author-X-Name-First: Gilles Author-X-Name-Last: Pagès Author-Name: Abass Sagna Author-X-Name-First: Abass Author-X-Name-Last: Sagna Title: Recursive Marginal Quantization of the Euler Scheme of a Diffusion Process Abstract: We propose a new approach to quantize the marginals of the discrete Euler diffusion process. The method is built recursively and involves the conditional distribution of the marginals of the discrete Euler process. Analytically, the method raises several questions like the analysis of the induced quadratic quantization error between the marginals of the Euler process and the proposed quantizations. We show in particular that at every discretization step tk of the Euler scheme, this error is bounded by the cumulative quantization errors induced by the Euler operator, from times t0 = 0 to time tk. For numerics, we restrict our analysis to the one-dimensional setting and show how to compute the optimal grids using a Newton-Raphson algorithm. We then propose a closed formula for the companion weights and the transition probabilities associated to the proposed quantizations. This allows us to quantize in particular diffusion processes in local volatility models by reducing dramatically the computational complexity of the search of optimal quantizers while increasing their computational precision with respect to the algorithms commonly proposed in this framework. Numerical tests are carried out for the Brownian motion and for the pricing of European options in a local volatility model. A comparison with the Monte Carlo simulations shows that the proposed method may sometimes be more efficient (w.r.t. both computational precision and time complexity) than the Monte Carlo method. Journal: Applied Mathematical Finance Pages: 463-498 Issue: 5 Volume: 22 Year: 2015 Month: 11 X-DOI: 10.1080/1350486X.2015.1091741 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1091741 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:5:p:463-498 Template-Type: ReDIF-Article 1.0 Author-Name: Min Park Author-X-Name-First: Min Author-X-Name-Last: Park Author-Name: Steven P. Clark Author-X-Name-First: Steven P. Author-X-Name-Last: Clark Title: A Reduced-Form Model for Valuing Bonds with Make-Whole Call Provisions Abstract: We develop a reduced-form valuation model for bonds with make-whole call provisions. Informed by the structural differences between callable bonds with fixed call prices and callable bonds with make-whole call provisions, we specify our reduced-form model so that the call spread depends inversely on the default intensity. Using a sample of make-whole callable bonds, we estimate the parameters of our model using the extended Kalman filter and compare the performance of our model with the performance of a well-known reduced-form model for fixed-price callable bonds. Journal: Applied Mathematical Finance Pages: 499-521 Issue: 6 Volume: 22 Year: 2015 Month: 12 X-DOI: 10.1080/1350486X.2015.1095643 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1095643 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:6:p:499-521 Template-Type: ReDIF-Article 1.0 Author-Name: Duy-Minh Dang Author-X-Name-First: Duy-Minh Author-X-Name-Last: Dang Author-Name: Kenneth R. Jackson Author-X-Name-First: Kenneth R. Author-X-Name-Last: Jackson Author-Name: Mohammadreza Mohammadi Author-X-Name-First: Mohammadreza Author-X-Name-Last: Mohammadi Title: Dimension and variance reduction for Monte Carlo methods for high-dimensional models in finance Abstract: One-way coupling often occurs in multi-dimensional models in finance. In this paper, we present a dimension reduction technique for Monte Carlo (MC) methods, referred to as drMC, that exploits this structure for pricing plain-vanilla European options under an N-dimensional one-way coupled model, where N is arbitrary. The dimension reduction also often produces a significant variance reduction.The drMC method is a dimension reduction technique built upon (i) the conditional MC technique applied to one of the factors which does not depend on any other factors in the model, and (ii) the derivation of a closed-form solution to the conditional partial differential equation (PDE) that arises via Fourier transforms. In the drMC approach, the option price can be computed simply by taking the expectation of this closed-form solution. Hence, the approach results in a powerful dimension reduction from N to one, which often results in a significant variance reduction as well, since the variance associated with the other factors in the original model are completely removed from the drMC simulation. Moreover, under the drMC framework, hedging parameters, or Greeks, can be computed in a much more efficient way than in traditional MC techniques. A variance reduction analysis of the method is presented and numerical results illustrating the method’s efficiency are provided. Journal: Applied Mathematical Finance Pages: 522-552 Issue: 6 Volume: 22 Year: 2015 Month: 12 X-DOI: 10.1080/1350486X.2015.1110492 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1110492 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:6:p:522-552 Template-Type: ReDIF-Article 1.0 Author-Name: Ming-Chi Chang Author-X-Name-First: Ming-Chi Author-X-Name-Last: Chang Author-Name: Yuan-Chung Sheu Author-X-Name-First: Yuan-Chung Author-X-Name-Last: Sheu Author-Name: Ming-Yao Tsai Author-X-Name-First: Ming-Yao Author-X-Name-Last: Tsai Title: Pricing Perpetual American Compound Options under a Matrix-Exponential Jump-Diffusion Model Abstract: This paper considers the problem of pricing perpetual American compound options under a matrix-exponential jump-diffusion model. The rational prices of these options are defined as the value functions of the corresponding optimal stopping problems. The general optimal stopping theory and the averaging method for solving the optimal stopping problems are applied to find the value functions and the optimal stopping times and thereby to determine the rational prices and the optimal boundaries of these perpetual American compound options. Explicit formulae for the rational prices and the optimal boundaries are also obtained for hyper-exponential jump-diffusion models. Journal: Applied Mathematical Finance Pages: 553-575 Issue: 6 Volume: 22 Year: 2015 Month: 12 X-DOI: 10.1080/1350486X.2015.1118354 File-URL: http://hdl.handle.net/10.1080/1350486X.2015.1118354 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:22:y:2015:i:6:p:553-575 Template-Type: ReDIF-Article 1.0 Author-Name: Djilali Ait Aoudia Author-X-Name-First: Djilali Author-X-Name-Last: Ait Aoudia Author-Name: Jean-François Renaud Author-X-Name-First: Jean-François Author-X-Name-Last: Renaud Title: Pricing Occupation-Time Options in a Mixed-Exponential Jump-Diffusion Model Abstract: In this short paper, in order to price occupation-time options, such as (double-barrier) step options and quantile options, we derive various joint distributions of a mixed-exponential jump-diffusion process and its occupation times of intervals. Journal: Applied Mathematical Finance Pages: 1-21 Issue: 1 Volume: 23 Year: 2016 Month: 3 X-DOI: 10.1080/1350486X.2016.1145066 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1145066 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:1:p:1-21 Template-Type: ReDIF-Article 1.0 Author-Name: Mark S. Joshi Author-X-Name-First: Mark S. Author-X-Name-Last: Joshi Author-Name: Dan Zhu Author-X-Name-First: Dan Author-X-Name-Last: Zhu Title: Optimal Partial Proxy Method for Computing Gammas of Financial Products with Discontinuous and Angular Payoffs Abstract: We extend the limit optimal partial proxy method to compute second-order sensitivities of financial products with discontinuous or angular payoffs by Monte Carlo simulation. The methodology is optimal in terms of minimizing the variance of the likelihood ratio weight. Applications are presented for both equity and interest-rate products with discontinuous payoff structures. The first-order optimal partial proxy method is also implemented to calculate the Hessians of insurance products with angular payoffs. Numerical results are presented which demonstrate the speed and efficacy of the method. Journal: Applied Mathematical Finance Pages: 22-56 Issue: 1 Volume: 23 Year: 2016 Month: 3 X-DOI: 10.1080/1350486X.2016.1156487 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1156487 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:1:p:22-56 Template-Type: ReDIF-Article 1.0 Author-Name: Christophe Michel Author-X-Name-First: Christophe Author-X-Name-Last: Michel Author-Name: Victor Reutenauer Author-X-Name-First: Victor Author-X-Name-Last: Reutenauer Author-Name: Denis Talay Author-X-Name-First: Denis Author-X-Name-Last: Talay Author-Name: Etienne Tanré Author-X-Name-First: Etienne Author-X-Name-Last: Tanré Title: Liquidity Costs: A New Numerical Methodology and an Empirical Study Abstract: We consider rate swaps which pay a fixed rate against a floating rate in the presence of bid-ask spread costs. Even for simple models of bid-ask spread costs, there is no explicit strategy optimizing an expected function of the hedging error. We here propose an efficient algorithm based on the stochastic gradient method to compute an approximate optimal strategy without solving a stochastic control problem. We validate our algorithm by numerical experiments. We also develop several variants of the algorithm and discuss their performances in terms of the numerical parameters and the liquidity cost. Journal: Applied Mathematical Finance Pages: 57-79 Issue: 1 Volume: 23 Year: 2016 Month: 3 X-DOI: 10.1080/1350486X.2016.1164608 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1164608 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:1:p:57-79 Template-Type: ReDIF-Article 1.0 Author-Name: Lorenzo Torricelli Author-X-Name-First: Lorenzo Author-X-Name-Last: Torricelli Title: Volatility Targeting Using Delayed Diffusions Abstract: A target volatility strategy (TVS) is a risky asset-riskless bond dynamic portfolio allocation which makes use of the risky asset historical volatility as an allocation rule with the aim of maintaining the instantaneous volatility of the investment constant at a target level. In a market with stochastic volatility, we consider a diffusion model for the value of a target volatility fund (TVF) which employs a system of stochastic delayed differential equations (SDDEs) involving the asset realized variance. First we prove that under some technical assumptions, contingent claim valuation on a TVF is approximately of Black-Scholes type, which is consistent with and supports the standing market practice. In second place, we develop a computational framework using recent results on Markovian approximations of SDDEs systems, which we then implement in the Heston variance model using an ad hoc Euler scheme. Our framework allows for efficient numerical valuation of derivatives on TVFs, whose typical purpose is the assessment of the guarantee costs of such funds for insurers. Journal: Applied Mathematical Finance Pages: 213-246 Issue: 3 Volume: 25 Year: 2018 Month: 5 X-DOI: 10.1080/1350486X.2018.1493390 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1493390 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:3:p:213-246 Template-Type: ReDIF-Article 1.0 Author-Name: Takuji Arai Author-X-Name-First: Takuji Author-X-Name-Last: Arai Author-Name: Yuto Imai Author-X-Name-First: Yuto Author-X-Name-Last: Imai Title: A numerically efficient closed-form representation of mean-variance hedging for exponential additive processes based on Malliavin calculus Abstract: We focus on mean-variance hedging problem for models whose asset price follows an exponential additive process. Some representations of mean-variance hedging strategies for jump-type models have already been suggested, but none is suited to develop numerical methods of the values of strategies for any given time up to the maturity. In this paper, we aim to derive a new explicit closed-form representation, which enables us to develop an efficient numerical method using the fast Fourier transforms. Note that our representation is described in terms of Malliavin derivatives. In addition, we illustrate numerical results for exponential Lévy models. Journal: Applied Mathematical Finance Pages: 247-267 Issue: 3 Volume: 25 Year: 2018 Month: 5 X-DOI: 10.1080/1350486X.2018.1506259 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1506259 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:3:p:247-267 Template-Type: ReDIF-Article 1.0 Author-Name: Ali Al-Aradi Author-X-Name-First: Ali Author-X-Name-Last: Al-Aradi Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Outperformance and Tracking: Dynamic Asset Allocation for Active and Passive Portfolio Management Abstract: Portfolio management problems are often divided into two types: active and passive, where the objective is to outperform and track a preselected benchmark, respectively. Here, we formulate and solve a dynamic asset allocation problem that combines these two objectives in a unified framework. We look to maximize the expected growth rate differential between the wealth of the investor’s portfolio and that of a performance benchmark while penalizing risk-weighted deviations from a given tracking portfolio. Using stochastic control techniques, we provide explicit closed-form expressions for the optimal allocation and we show how the optimal strategy can be related to the growth optimal portfolio. The admissible benchmarks encompass the class of functionally generated portfolios (FGPs), which include the market portfolio, as the only requirement is that they depend only on the prevailing asset values. Finally, some numerical experiments are presented to illustrate the risk–reward profile of the optimal allocation. Journal: Applied Mathematical Finance Pages: 268-294 Issue: 3 Volume: 25 Year: 2018 Month: 5 X-DOI: 10.1080/1350486X.2018.1507751 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1507751 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:3:p:268-294 Template-Type: ReDIF-Article 1.0 Author-Name: Mohammed Berkhouch Author-X-Name-First: Mohammed Author-X-Name-Last: Berkhouch Author-Name: Ghizlane Lakhnati Author-X-Name-First: Ghizlane Author-X-Name-Last: Lakhnati Author-Name: Marcelo Brutti Righi Author-X-Name-First: Marcelo Brutti Author-X-Name-Last: Righi Title: Extended Gini-Type Measures of Risk and Variability Abstract: The aim of this paper is to introduce a risk measure, Extended Gini Shortfall (EGS), that extends the Gini-type measures of risk and variability by taking risk aversion into consideration. Our risk measure is coherent and catches variability, an important concept for risk management. The analysis is made under the Choquet integral representations framework. We expose results for analytic computation under well-known distribution functions. Furthermore, we provide a practical application. Journal: Applied Mathematical Finance Pages: 295-314 Issue: 3 Volume: 25 Year: 2018 Month: 5 X-DOI: 10.1080/1350486X.2018.1538806 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1538806 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:3:p:295-314 Template-Type: ReDIF-Article 1.0 Author-Name: Jan Pospíšil Author-X-Name-First: Jan Author-X-Name-Last: Pospíšil Author-Name: Tomáš Sobotka Author-X-Name-First: Tomáš Author-X-Name-Last: Sobotka Title: Market calibration under a long memory stochastic volatility model Abstract: In this article, we study a long memory stochastic volatility model (LSV), under which stock prices follow a jump-diffusion stochastic process and its stochastic volatility is driven by a continuous-time fractional process that attains a long memory. LSV model should take into account most of the observed market aspects and unlike many other approaches, the volatility clustering phenomenon is captured explicitly by the long memory parameter. Moreover, this property has been reported in realized volatility time-series across different asset classes and time periods. In the first part of the article, we derive an alternative formula for pricing European securities. The formula enables us to effectively price European options and to calibrate the model to a given option market. In the second part of the article, we provide an empirical review of the model calibration. For this purpose, a set of traded FTSE 100 index call options is used and the long memory volatility model is compared to a popular pricing approach – the Heston model. To test stability of calibrated parameters and to verify calibration results from previous data set, we utilize multiple data sets from NYSE option market on Apple Inc. stock. Journal: Applied Mathematical Finance Pages: 323-343 Issue: 5 Volume: 23 Year: 2016 Month: 9 X-DOI: 10.1080/1350486X.2017.1279977 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1279977 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:5:p:323-343 Template-Type: ReDIF-Article 1.0 Author-Name: Wendong Zheng Author-X-Name-First: Wendong Author-X-Name-Last: Zheng Author-Name: Pingping Zeng Author-X-Name-First: Pingping Author-X-Name-Last: Zeng Title: Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model Abstract: Most of the empirical studies on stochastic volatility dynamics favour the 3/2 specification over the square-root (CIR) process in the Heston model. In the context of option pricing, the 3/2 stochastic volatility model (SVM) is reported to be able to capture the volatility skew evolution better than the Heston model. In this article, we make a thorough investigation on the analytic tractability of the 3/2 SVM by proposing a closed-form formula for the partial transform of the triple joint transition density $$(X,I,V)$$(X,I,V) which stand for the log asset price, the quadratic variation (continuous realized variance) and the instantaneous variance, respectively. Two distinct formulations are provided for deriving the main result. The closed-form partial transform enables us to deduce a variety of marginal partial transforms and characteristic functions and plays a crucial role in pricing discretely sampled variance derivatives and exotic options that depend on both the asset price and quadratic variation. Various applications and numerical examples on pricing moment swaps and timer options with discrete monitoring feature are given to demonstrate the versatility of the partial transform under the 3/2 model. Journal: Applied Mathematical Finance Pages: 344-373 Issue: 5 Volume: 23 Year: 2016 Month: 9 X-DOI: 10.1080/1350486X.2017.1285242 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1285242 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:5:p:344-373 Template-Type: ReDIF-Article 1.0 Author-Name: A. Papanicolaou Author-X-Name-First: A. Author-X-Name-Last: Papanicolaou Title: Analysis of VIX Markets with a Time-Spread Portfolio Abstract: This paper explores the relationship between option markets for the S&P500 (SPX) and Chicago Board Options Exchange’s CBOE’s Volatility Index (VIX). Results are obtained by using the so-called time-spread portfolio to replicate a future contract on the squared VIX. The time-spread portfolio is interesting because it provides a model-free link between derivative prices for SPX and VIX. Time spreads can be computed from SPX put options with different maturities, which results in a term structure for squared volatility. This term structure can be compared to the VIX-squared term structure that is backed-out from VIX call options. The time-spread portfolio is also used to measure volatility-of-volatility (vol-of-vol) and the volatility leverage effect. There may emerge small differences in these measurements, depending on whether time spreads are computed with options on SPX or options on VIX. A study of 2012 daily options data shows that vol-of-vol estimates utilizing SPX data will reflect the volatility leverage effect, whereas estimates that exclusively utilize VIX options will predominantly reflect the premia in the VIX-future term structure. Journal: Applied Mathematical Finance Pages: 374-408 Issue: 5 Volume: 23 Year: 2016 Month: 9 X-DOI: 10.1080/1350486X.2017.1290534 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1290534 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:5:p:374-408 Template-Type: ReDIF-Article 1.0 Author-Name: Damien Challet Author-X-Name-First: Damien Author-X-Name-Last: Challet Title: Sharper asset ranking from total drawdown durations Abstract: The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distribution tail exponent. The heterogeneity of tail exponents at any given time among assets implies that our new method yields significantly different asset rankings than those of moment-based methods, especially in periods large volatility. This is fully confirmed by using 20 years of historical data on 3449 liquid US equities. Journal: Applied Mathematical Finance Pages: 1-22 Issue: 1 Volume: 24 Year: 2017 Month: 1 X-DOI: 10.1080/1350486X.2017.1297728 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1297728 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:1:p:1-22 Template-Type: ReDIF-Article 1.0 Author-Name: David Criens Author-X-Name-First: David Author-X-Name-Last: Criens Author-Name: Kathrin Glau Author-X-Name-First: Kathrin Author-X-Name-Last: Glau Author-Name: Zorana Grbac Author-X-Name-First: Zorana Author-X-Name-Last: Grbac Title: Martingale property of exponential semimartingales: a note on explicit conditions and applications to asset price and Libor models Abstract: We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very convenient in financial modelling in general. Especially it allows us to carefully discuss the question of well-definedness of semimartingale Libor models, whose construction crucially relies on a sequence of measure changes. Journal: Applied Mathematical Finance Pages: 23-37 Issue: 1 Volume: 24 Year: 2017 Month: 1 X-DOI: 10.1080/1350486X.2017.1327324 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1327324 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:1:p:23-37 Template-Type: ReDIF-Article 1.0 Author-Name: Stéphane Goutte Author-X-Name-First: Stéphane Author-X-Name-Last: Goutte Author-Name: Amine Ismail Author-X-Name-First: Amine Author-X-Name-Last: Ismail Author-Name: Huyên Pham Author-X-Name-First: Huyên Author-X-Name-Last: Pham Title: Regime-switching stochastic volatility model: estimation and calibration to VIX options Abstract: We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a Cox–Ingersoll–Ross process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum–Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices. Journal: Applied Mathematical Finance Pages: 38-75 Issue: 1 Volume: 24 Year: 2017 Month: 1 X-DOI: 10.1080/1350486X.2017.1333015 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1333015 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:1:p:38-75 Template-Type: ReDIF-Article 1.0 Author-Name: Ryan Donnelly Author-X-Name-First: Ryan Author-X-Name-Last: Donnelly Author-Name: Luhui Gan Author-X-Name-First: Luhui Author-X-Name-Last: Gan Title: Optimal Decisions in a Time Priority Queue Abstract: We show how the position of a limit order (LO) in the queue influences the decision of whether to cancel the order or let it rest. Using ultra-high-frequency data from the Nasdaq exchange, we perform empirical analysis on various LO book events and propose novel ways for modelling some of these events, including cancellation of LOs in various positions and size of market orders. Based on our empirical findings, we develop a queuing model that captures stylized facts on the data. This model includes a distinct feature which allows for a potentially random effect due to the agent’s impulse control. We apply the queuing model in an algorithmic trading setting by considering an agent maximizing her expected utility through placing and cancelling of LOs. The agent’s optimal strategy is presented after calibrating the model to real data. A simulation study shows that for the same level of standard deviation of terminal wealth, the optimal strategy has a 2.5% higher mean compared to a strategy which ignores the effect of position, or an 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting an LO during adverse conditions and obtaining a good queue position before conditions become favourable. Journal: Applied Mathematical Finance Pages: 107-147 Issue: 2 Volume: 25 Year: 2018 Month: 3 X-DOI: 10.1080/1350486X.2018.1506257 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1506257 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:2:p:107-147 Template-Type: ReDIF-Article 1.0 Author-Name: Julien Baptiste Author-X-Name-First: Julien Author-X-Name-Last: Baptiste Author-Name: Julien Grepat Author-X-Name-First: Julien Author-X-Name-Last: Grepat Author-Name: Emmanuel Lepinette Author-X-Name-First: Emmanuel Author-X-Name-Last: Lepinette Title: Approximation of Non-Lipschitz SDEs by Picard Iterations Abstract: In this article, we propose an approximation method based on Picard iterations deduced from the Doléans–Dade exponential formula. Our method allows to approximate trajectories of Markov processes in a large class, e.g., solutions to non-Lipchitz stochastic differential equation. An application to the pricing of Asian-style contingent claims in the constant elasticity of variance model is presented and compared to other methods of the literature. Journal: Applied Mathematical Finance Pages: 148-179 Issue: 2 Volume: 25 Year: 2018 Month: 3 X-DOI: 10.1080/1350486X.2018.1507749 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1507749 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:2:p:148-179 Template-Type: ReDIF-Article 1.0 Author-Name: Tim Leung Author-X-Name-First: Tim Author-X-Name-Last: Leung Author-Name: Brian Ward Author-X-Name-First: Brian Author-X-Name-Last: Ward Title: Dynamic Index Tracking and Risk Exposure Control Using Derivatives Abstract: We develop a methodology for index tracking and risk exposure control using financial derivatives. Under a continuous-time diffusion framework for price evolution, we present a pathwise approach to construct dynamic portfolios of derivatives in order to gain exposure to an index and/or market factors that may be not directly tradable. Among our results, we establish a general tracking condition that relates the portfolio drift to the desired exposure coefficients under any given model. We also derive a slippage process that reveals how the portfolio return deviates from the targeted return. In our multi-factor setting, the portfolio’s realized slippage depends not only on the realized variance of the index but also the realized covariance among the index and factors. We implement our trading strategies under a number of models, and compare the tracking strategies and performances when using different derivatives, such as futures and options. Journal: Applied Mathematical Finance Pages: 180-212 Issue: 2 Volume: 25 Year: 2018 Month: 3 X-DOI: 10.1080/1350486X.2018.1507750 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1507750 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:2:p:180-212 Template-Type: ReDIF-Article 1.0 Author-Name: Johannes Ruf Author-X-Name-First: Johannes Author-X-Name-Last: Ruf Author-Name: Kangjianan Xie Author-X-Name-First: Kangjianan Author-X-Name-Last: Xie Title: Generalised Lyapunov Functions and Functionally Generated Trading Strategies Abstract: This paper investigates the dependence of functional portfolio generation, introduced by Fernholz (1999), on an extra finite variation process. The framework of Karatzas and Ruf (2017) is used to formulate conditions on trading strategies to be strong arbitrage relative to the market over sufficiently large time horizons. A mollification argument and Komlós theorem yield a general class of potential arbitrage strategies. These theoretical results are complemented by several empirical examples using data from the S&P 500 stocks. Journal: Applied Mathematical Finance Pages: 293-327 Issue: 4 Volume: 26 Year: 2019 Month: 7 X-DOI: 10.1080/1350486X.2019.1584041 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1584041 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:4:p:293-327 Template-Type: ReDIF-Article 1.0 Author-Name: Jorge Guijarro-Ordonez Author-X-Name-First: Jorge Author-X-Name-Last: Guijarro-Ordonez Title: High-dimensional Statistical Arbitrage with Factor Models and Stochastic Control Abstract: The present paper provides a study of high-dimensional statistical arbitrage that combines factor models with the tools from stochastic control, obtaining closed-form optimal strategies which are both interpretable and computationally implementable in a high-dimensional setting. Our setup is based on a general statistically constructed factor model with mean-reverting residuals, in which we show how to construct analytically market-neutral portfolios and we analyse the problem of investing optimally in continuous time and finite horizon under exponential and mean-variance utilities. We also extend our model to incorporate constraints on the investor’s portfolio like dollar-neutrality and market frictions in the form of temporary quadratic transaction costs, provide extensive Monte Carlo simulations of the previous strategies with 100 assets, and describe further possible extensions of our work. Journal: Applied Mathematical Finance Pages: 328-358 Issue: 4 Volume: 26 Year: 2019 Month: 7 X-DOI: 10.1080/1350486X.2019.1702067 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1702067 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:4:p:328-358 Template-Type: ReDIF-Article 1.0 Author-Name: Guglielmo D’Amico Author-X-Name-First: Guglielmo Author-X-Name-Last: D’Amico Author-Name: Filippo Petroni Author-X-Name-First: Filippo Author-X-Name-Last: Petroni Author-Name: Philippe Regnault Author-X-Name-First: Philippe Author-X-Name-Last: Regnault Author-Name: Stefania Scocchera Author-X-Name-First: Stefania Author-X-Name-Last: Scocchera Author-Name: Loriano Storchi Author-X-Name-First: Loriano Author-X-Name-Last: Storchi Title: A Copula-based Markov Reward Approach to the Credit Spread in the European Union Abstract: In this paper, we propose a methodology based on piecewise homogeneous Markov chain for credit ratings and a multivariate model of the credit spreads to evaluate the financial risk in the European Union (EU). Two main aspects are considered: how the financial risk is distributed among the European countries and how large is the value of the total risk. The first aspect is evaluated by means of the expected value of a dynamic entropy measure. The second one is solved by computing the evolution of the total credit spread over time. Moreover, the covariance between countries’ total spread allows the understanding of any contagions in the EU. The methodology is applied to real data of 24 European countries for the three major rating agencies: Moody’s, Standard & Poor’s and Fitch. Obtained results suggest that both the financial risk inequality and the value of the total risk increase over time at a different rate depending on the rating agency. Moreover, the results indicate that the dependence structure is characterized by a strong correlation between most of the European countries. Journal: Applied Mathematical Finance Pages: 359-386 Issue: 4 Volume: 26 Year: 2019 Month: 7 X-DOI: 10.1080/1350486X.2019.1702068 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1702068 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:4:p:359-386 Template-Type: ReDIF-Article 1.0 Author-Name: Etienne Chevalier Author-X-Name-First: Etienne Author-X-Name-Last: Chevalier Author-Name: Thomas Lim Author-X-Name-First: Thomas Author-X-Name-Last: Lim Author-Name: Ricardo Romo Romero Author-X-Name-First: Ricardo Author-X-Name-Last: Romo Romero Title: Indifference fee rate for variable annuities Abstract: In this paper, we work on indifference valuation of variable annuities and give a computation method for indifference fees. We focus on the guaranteed minimum death benefits (GMDB) and the guaranteed minimum living benefits (GMLB) and allow the policyholder to make withdrawals. We assume that the fees are continuously paid and that the fee rate is fixed at the beginning of the contract. Following indifference pricing theory, we define indifference fee rate for the insurer as a solution of an equation involving two stochastic control problems. Relating these problems to backward stochastic differential equations (BSDEs) with jumps, we provide a verification theorem and give the optimal strategies associated to our control problems. From these, we derive a computation method to get indifference fee rates. We conclude our work with numerical illustrations of indifference fees sensibilities with respect to parameters. Journal: Applied Mathematical Finance Pages: 278-308 Issue: 4 Volume: 23 Year: 2016 Month: 7 X-DOI: 10.1080/1350486X.2016.1243011 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1243011 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:4:p:278-308 Template-Type: ReDIF-Article 1.0 Author-Name: Jostein Tvedt Author-X-Name-First: Jostein Author-X-Name-Last: Tvedt Title: Closed form equilibrium evaluation of interest rate caps and related derivatives in a real business cycle setting Abstract: The objective of this study is to provide closed form solutions to financial derivatives on mean-reverting cash flows. The general equilibrium real business cycle specification implies that underlying prices follow geometric mean reversion processes. Option-pricing formulas are derived, in terms of macroeconomic parameters or observable market prices, both for consumption goods and interest rates. The framework offers a rich specification of the economy’s yield curve and caplet volatility surface, which seems to fit well with criteria suggested by the empirical literature. The methodology may be useful for studying the effects of real economy changes on financial markets. Journal: Applied Mathematical Finance Pages: 261-277 Issue: 4 Volume: 23 Year: 2016 Month: 7 X-DOI: 10.1080/1350486X.2016.1243012 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1243012 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:4:p:261-277 Template-Type: ReDIF-Article 1.0 Author-Name: Young Shin Kim Author-X-Name-First: Young Author-X-Name-Last: Shin Kim Title: Long-Range Dependence in the Risk-Neutral Measure for the Market on Lehman Brothers Collapse Abstract: This paper discusses the long-range dependence in the risk-neutral stock return process of the S&P 500 index option market. To observe the long-range dependence together with fat-tails, I define the parametric model of fractional Lévy process. Since the continuous time fractional Lévy process allows arbitrage, I use discrete time option pricing model based on the fractional Lévy process. By model calibration, we can capture the long-range dependence in the S&P 500 index option market. The paper finds that the long range dependence becomes stronger for the volatile market caused by the Lehman Brothers Collapse, comparing with other less volatility markets. Journal: Applied Mathematical Finance Pages: 309-322 Issue: 4 Volume: 23 Year: 2016 Month: 7 X-DOI: 10.1080/1350486X.2016.1268926 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1268926 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:4:p:309-322 Template-Type: ReDIF-Article 1.0 Author-Name: Álvaro Cartea Author-X-Name-First: Álvaro Author-X-Name-Last: Cartea Author-Name: Ryan Donnelly Author-X-Name-First: Ryan Author-X-Name-Last: Donnelly Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Enhancing trading strategies with order book signals Abstract: We use high-frequency data from the Nasdaq exchange to build a measure of volume imbalance in the limit order (LO) book. We show that our measure is a good predictor of the sign of the next market order (MO), i.e., buy or sell, and also helps to predict price changes immediately after the arrival of an MO. Based on these empirical findings, we introduce and calibrate a Markov chain-modulated pure jump model of price, spread, LO and MO arrivals and volume imbalance. As an application of the model, we pose and solve a stochastic control problem for an agent who maximizes terminal wealth, subject to inventory penalties, by executing trades using LOs. We use in-sample-data (January to June 2014) to calibrate the model to 11 equities traded in the Nasdaq exchange and use out-of-sample data (July to December 2014) to test the performance of the strategy. We show that introducing our volume imbalance measure into the optimization problem considerably boosts the profits of the strategy. Profits increase because employing our imbalance measure reduces adverse selection costs and positions LOs in the book to take advantage of favourable price movements. Journal: Applied Mathematical Finance Pages: 1-35 Issue: 1 Volume: 25 Year: 2018 Month: 1 X-DOI: 10.1080/1350486X.2018.1434009 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1434009 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:1:p:1-35 Template-Type: ReDIF-Article 1.0 Author-Name: Fred Espen Benth Author-X-Name-First: Fred Espen Author-X-Name-Last: Benth Author-Name: Anca Pircalabu Author-X-Name-First: Anca Author-X-Name-Last: Pircalabu Title: A non-Gaussian Ornstein–Uhlenbeck model for pricing wind power futures Abstract: The recent introduction of wind power futures written on the German wind power production index has brought with it new interesting challenges in terms of modelling and pricing. Some particularities of this product are the strong seasonal component embedded in the underlying, the fact that the wind index is bounded from both above and below and also that the futures are settled against a synthetically generated spot index. Here, we consider the non-Gaussian Ornstein–Uhlenbeck type processes proposed by Barndorff-Nielsen and Shephard in the context of modelling the wind power production index. We discuss the properties of the model and estimation of the model parameters. Further, the model allows for an analytical formula for pricing wind power futures. We provide an empirical study, where the model is calibrated to 37 years of German wind power production index that is synthetically generated assuming a constant level of installed capacity. Also, based on 1 year of observed prices for wind power futures with different delivery periods, we study the market price of risk. Generally, we find a negative risk premium whose magnitude decreases as the length of the delivery period increases. To further demonstrate the benefits of our proposed model, we address the pricing of European options written on wind power futures, which can be achieved through Fourier techniques. Journal: Applied Mathematical Finance Pages: 36-65 Issue: 1 Volume: 25 Year: 2018 Month: 1 X-DOI: 10.1080/1350486X.2018.1438904 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1438904 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:1:p:36-65 Template-Type: ReDIF-Article 1.0 Author-Name: Irène Gijbels Author-X-Name-First: Irène Author-X-Name-Last: Gijbels Author-Name: Klaus Herrmann Author-X-Name-First: Klaus Author-X-Name-Last: Herrmann Title: Optimal Expected-Shortfall Portfolio Selection with Copula-Induced Dependence Abstract: We provide a computational framework for the selection of weights $$({\omega _1}, \ldots ,{\omega _d})$$(ω1,…,ωd) that minimize the expected shortfall of the aggregated risk $$Z = \mathop \sum \nolimits_{i = 1}^d {\omega _i}{X_i}$$Z=∑i=1dωiXi . Contrary to classic and recent results, we neither restrict the marginal distributions nor the dependence structure of $$({X_1}, \ldots ,{X_d})$$(X1,…,Xd) to any specific type. While the margins can be set to any absolutely continuous random variable with finite expectation, the dependence structure can be modelled by any absolutely continuous copula function. A real-world application to portfolio selection illustrates the usability of the new framework. Journal: Applied Mathematical Finance Pages: 66-106 Issue: 1 Volume: 25 Year: 2018 Month: 1 X-DOI: 10.1080/1350486X.2018.1492347 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1492347 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:1:p:66-106 Template-Type: ReDIF-Article 1.0 Author-Name: Gary Quek Author-X-Name-First: Gary Author-X-Name-Last: Quek Author-Name: Colin Atkinson Author-X-Name-First: Colin Author-X-Name-Last: Atkinson Title: Portfolio selection in discrete time with transaction costs and power utility function: a perturbation analysis Abstract: In this article, we study a multi-period portfolio selection model in which a generic class of probability distributions is assumed for the returns of the risky asset. An investor with a power utility function rebalances a portfolio comprising a risk-free and risky asset at the beginning of each time period in order to maximize expected utility of terminal wealth. Trading the risky asset incurs a cost that is proportional to the value of the transaction. At each time period, the optimal investment strategy involves buying or selling the risky asset to reach the boundaries of a certain no-transaction region. In the limit of small transaction costs, dynamic programming and perturbation analysis are applied to obtain explicit approximations to the optimal boundaries and optimal value function of the portfolio at each stage of a multi-period investment process of any length. Journal: Applied Mathematical Finance Pages: 77-111 Issue: 2 Volume: 24 Year: 2017 Month: 3 X-DOI: 10.1080/1350486X.2017.1342551 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1342551 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:2:p:77-111 Template-Type: ReDIF-Article 1.0 Author-Name: Olivier Guéant Author-X-Name-First: Olivier Author-X-Name-Last: Guéant Title: Optimal market making Abstract: Market makers provide liquidity to other market participants: they propose prices at which they stand ready to buy and sell a wide variety of assets. They face a complex optimization problem with both static and dynamic components. They need indeed to propose bid and offer/ask prices in an optimal way for making money out of the difference between these two prices (their bid–ask spread). Since they seldom buy and sell simultaneously, and therefore hold long and/or short inventories, they also need to mitigate the risk associated with price changes and subsequently skew their quotes dynamically. In this paper, (i) we propose a general modelling framework which generalizes (and reconciles) the various modelling approaches proposed in the literature since the publication of the seminal paper ‘High-frequency trading in a limit order book’ by Avellaneda and Stoikov, (ii) we prove new general results on the existence and the characterization of optimal market making strategies, (iii) we obtain new closed-form approximations for the optimal quotes, (iv) we extend the modelling framework to the case of multi-asset market making and we obtain general closed-form approximations for the optimal quotes of a multi-asset market maker, and (v) we show how the model can be used in practice in the specific (and original) case of two credit indices. Journal: Applied Mathematical Finance Pages: 112-154 Issue: 2 Volume: 24 Year: 2017 Month: 3 X-DOI: 10.1080/1350486X.2017.1342552 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1342552 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:2:p:112-154 Template-Type: ReDIF-Article 1.0 Author-Name: Dilip B. Madan Author-X-Name-First: Dilip B. Author-X-Name-Last: Madan Title: Financial jeopardy Abstract: Learning the pre-limited liability value process of equity claims and its relationship to the stock price is an answer to the financial jeopardy question when observed option prices are the answer being given by the market. Constant dollar equity holder values, prior to the imposition of limited liability, are the signed conditional expectations of the integral of discounted net residual equity claims through all time. The stock is modelled as a limited liability claim imputing positive dividend flows to shareholders in certain circumstances coupled with a call option written on the integral of all discounted net residual equity claims. The underlying signed value has a known characteristic function when revenues and expenses are modelled as independent gamma processes. The stock price is a positive function of this signed underlying value, given by the solution of a partial integro differential equation. Options on the stock are then options on this function of the signed underlying value and are solved for using its density obtained by Fourier inversion of the characteristic function. The calibration of model parameters, the imputed dividend function and the terminal call strike is conducted on option prices at a single maturity for four underliers, AMZN, SPY, GOOG and JNJ. In all these cases it is observed that risk neutrally up moves arrive more frequently and are generally smaller while down moves are less frequent and are larger. The terminal option strikes were in the money for SPY and JNJ, and out of the money for AMZN and GOOG. Journal: Applied Mathematical Finance Pages: 155-173 Issue: 2 Volume: 24 Year: 2017 Month: 3 X-DOI: 10.1080/1350486X.2017.1353917 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1353917 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:2:p:155-173 Template-Type: ReDIF-Article 1.0 Author-Name: J. C. Arismendi Author-X-Name-First: J. C. Author-X-Name-Last: Arismendi Author-Name: Marcel Prokopczuk Author-X-Name-First: Marcel Author-X-Name-Last: Prokopczuk Title: A moment-based analytic approximation of the risk-neutral density of American options Abstract: The price of a European option can be computed as the expected value of the payoff function under the risk-neutral measure. For American options and path-dependent options in general, this principle cannot be applied. In this paper, we derive a model-free analytical formula for the implied risk-neutral density based on the implied moments of the implicit European contract under which the expected value will be the price of the equivalent payoff with the American exercise condition. The risk-neutral density is semi-parametric as it is the result of applying the multivariate generalized Edgeworth expansion, where the moments of the American density are obtained by a reverse engineering application of the least-squares method. The theory of multivariate truncated moments is employed for approximating the option price, with important consequences for the hedging of variance, skewness and kurtosis swaps. Journal: Applied Mathematical Finance Pages: 409-444 Issue: 6 Volume: 23 Year: 2016 Month: 11 X-DOI: 10.1080/1350486X.2017.1297726 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1297726 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:6:p:409-444 Template-Type: ReDIF-Article 1.0 Author-Name: Dan Pirjol Author-X-Name-First: Dan Author-X-Name-Last: Pirjol Title: Eurodollar futures pricing in log-normal interest rate models in discrete time Abstract: We demonstrate the appearance of explosions in three quantities in interest rate models with log-normally distributed rates in discrete time. (1) The expectation of the money market account in the Black, Derman, Toy model, (2) the prices of Eurodollar futures contracts in a model with log-normally distributed rates in the terminal measure and (3) the prices of Eurodollar futures contracts in the one-factor log-normal Libor market model (LMM). We derive exact upper and lower bounds on the prices and on the standard deviation of the Monte Carlo pricing of Eurodollar futures in the one factor log-normal Libor market model. These bounds explode at a non-zero value of volatility, and thus imply a limitation on the applicability of the LMM and on its Monte Carlo simulation to sufficiently low volatilities. Journal: Applied Mathematical Finance Pages: 445-464 Issue: 6 Volume: 23 Year: 2016 Month: 11 X-DOI: 10.1080/1350486X.2017.1297727 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1297727 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:6:p:445-464 Template-Type: ReDIF-Article 1.0 Author-Name: T. De Angelis Author-X-Name-First: T. Author-X-Name-Last: De Angelis Author-Name: G. Peskir Author-X-Name-First: G. Author-X-Name-Last: Peskir Title: Optimal prediction of resistance and support levels Abstract: Assuming that the asset price X follows a geometric Brownian motion, we study the optimal prediction problem$$\mathop {\inf }\limits_{0\,\le\,\tau\,\le\;T} {\mathfrak{E}}\,\left| {X_\tau ^x - \ell } \right|$$inf0≤τ≤TEXτx−ℓ where the infimum is taken over stopping times $$\tau $$τ of X and $$\ell $$ℓ is a hidden aspiration level (having a potential of creating a resistance or support level for X). Adopting the ‘aspiration-level hypothesis’ and assuming that $$\ell $$ℓ is independent from X, we show that a wide class of admissible (non-oscillatory) laws of $$\ell $$ℓ lead to unique optimal trading boundaries that can be viewed as the ‘conditional median curves’ for the resistance and support levels (with respect to X and T). We prove the existence of these boundaries and derive the (nonlinear) integral equations which characterize them uniquely. The results are illustrated through some specific examples of admissible laws and their conditional median curves. Journal: Applied Mathematical Finance Pages: 465-483 Issue: 6 Volume: 23 Year: 2016 Month: 11 X-DOI: 10.1080/1350486X.2017.1297729 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1297729 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:6:p:465-483 Template-Type: ReDIF-Article 1.0 Author-Name: Thorsten Lehnert Author-X-Name-First: Thorsten Author-X-Name-Last: Lehnert Author-Name: Yuehao Lin Author-X-Name-First: Yuehao Author-X-Name-Last: Lin Title: Skewness Term-Structure Tests Abstract: In this paper, we conduct skewness term-structure tests to check whether the temporal structure of risk-neutral skewness is consistent with rational expectations. Because risk-neutral skewness is substantially mean reverting, skewness shocks should decay quickly and risk-neutral skewness of more distant option should display the rationally expected smoothing behaviour. Using an equilibrium asset and option-pricing model in a production economy under jump diffusion with stochastic jump intensity, we derive this elasticity analytically. In an empirical application of the model using more than 20 years of data on S&P500 index options, we find that this elasticity turns out to be different than suggested under rational expectations – smaller on the short end (underreaction) and larger on the long end (overreaction) of the ‘skewness curve’. Journal: Applied Mathematical Finance Pages: 484-504 Issue: 6 Volume: 23 Year: 2016 Month: 11 X-DOI: 10.1080/1350486X.2017.1310624 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1310624 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:6:p:484-504 Template-Type: ReDIF-Article 1.0 Author-Name: Duy-Minh Dang Author-X-Name-First: Duy-Minh Author-X-Name-Last: Dang Author-Name: Kenneth R. Jackson Author-X-Name-First: Kenneth R. Author-X-Name-Last: Jackson Author-Name: Scott Sues Author-X-Name-First: Scott Author-X-Name-Last: Sues Title: A dimension and variance reduction Monte-Carlo method for option pricing under jump-diffusion models Abstract: We develop a highly efficient MC method for computing plain vanilla European option prices and hedging parameters under a very general jump-diffusion option pricing model which includes stochastic variance and multi-factor Gaussian interest short rate(s). The focus of our MC approach is variance reduction via dimension reduction. More specifically, the option price is expressed as an expectation of a unique solution to a conditional Partial Integro-Differential Equation (PIDE), which is then solved using a Fourier transform technique. Important features of our approach are (1) the analytical tractability of the conditional PIDE is fully determined by that of the Black–Scholes–Merton model augmented with the same jump component as in our model, and (2) the variances associated with all the interest rate factors are completely removed when evaluating the expectation via iterated conditioning applied to only the Brownian motion associated with the variance factor. For certain cases when numerical methods are either needed or preferred, we propose a discrete fast Fourier transform method to numerically solve the conditional PIDE efficiently. Our method can also effectively compute hedging parameters. Numerical results show that the proposed method is highly efficient. Journal: Applied Mathematical Finance Pages: 175-215 Issue: 3 Volume: 24 Year: 2017 Month: 5 X-DOI: 10.1080/1350486X.2017.1358646 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1358646 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:3:p:175-215 Template-Type: ReDIF-Article 1.0 Author-Name: S. Jaimungal Author-X-Name-First: S. Author-X-Name-Last: Jaimungal Author-Name: D. Kinzebulatov Author-X-Name-First: D. Author-X-Name-Last: Kinzebulatov Author-Name: D. H. Rubisov Author-X-Name-First: D. H. Author-X-Name-Last: Rubisov Title: Optimal accelerated share repurchases Abstract: An accelerated share repurchase allows a firm to repurchase a significant portion of its shares immediately, while shifting the burden of reducing the impact and uncertainty in the trade to an intermediary. The intermediary must then purchase the shares from the market over several days, weeks or as much as several months. Some contracts allow the intermediary to specify when the repurchase ends, at which point the firm and the intermediary exchange the difference between the arrival price and the TWAP over the trading period plus a spread. Hence, the intermediary effectively has an American option embedded within an optimal execution problem. As a result, the firm receives a discounted spread relative to the no early exercise case. Here, we address the intermediary’s optimal execution and exit strategy taking into account the impact that trading has on the market. We demonstrate that it is optimal to exercise when the TWAP exceeds $$\zeta (t,{q_t}){\kern 1pt} {S_t}$$ζ(t,qt)St where $${S_t}$$St is the midprice of the asset and $$\zeta $$ζ is a deterministic function of time and inventory. Moreover, we develop a dimensional reduction of the stochastic control and stopping problem and implement an efficient numerical scheme to compute the optimal trading and exit strategies. We also provide bounds on the optimal strategy and characterize the convexity and monotonicity of the optimal strategies in addition to exploring its behaviour numerically and through simulation studies. Journal: Applied Mathematical Finance Pages: 216-245 Issue: 3 Volume: 24 Year: 2017 Month: 5 X-DOI: 10.1080/1350486X.2017.1374870 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1374870 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:3:p:216-245 Template-Type: ReDIF-Article 1.0 Author-Name: Erindi Allaj Author-X-Name-First: Erindi Author-X-Name-Last: Allaj Title: Risk measuring under liquidity risk Abstract: We present a general framework for measuring the liquidity risk. The theoretical framework defines risk measures that incorporate the liquidity risk into the standard risk measures. We consider a one-period risk measurement model. The liquidity risk is defined as the risk that a security or a portfolio of securities cannot be sold or bought without causing changes in prices. The risk measures are decomposed into two terms, one measuring the risk of the future value of a given position in a security or a portfolio of securities and the other the initial cost of this position. Within the framework of coherent risk measures, the risk measures applied to the random part of the future value of a position in a determinate security are increasing monotonic and convex cash sub-additive on long positions. The contrary, in certain situations, holds for the sell positions. By using convex risk measures, we apply our framework to the situation in which large trades are broken into many small ones. Dual representation results are obtained for both positions in securities and portfolios. We give many examples of risk measures and derive for each of them the respective capital requirement. In particular, we discuss the VaR measure. Journal: Applied Mathematical Finance Pages: 246-279 Issue: 3 Volume: 24 Year: 2017 Month: 5 X-DOI: 10.1080/1350486X.2017.1374871 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1374871 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:3:p:246-279 Template-Type: ReDIF-Article 1.0 Author-Name: Stefan Waldenberger Author-X-Name-First: Stefan Author-X-Name-Last: Waldenberger Title: The affine inflation market models Abstract: Interest rate market models, such as the LIBOR market model, have the advantage that the basic model quantities are directly observable in financial markets. Inflation market models extend this approach to inflation markets, where two types of swaps, zero-coupon and year-on-year inflation-indexed swaps, are the basic observable products. For inflation market models considered so far, closed formulas exist for only one type of swap, but not for both. The model in this paper uses affine processes in such a way that prices for both types of swaps can be calculated explicitly. Furthermore, call and put options on both types of swap rates can be calculated using one-dimensional Fourier inversion formulas. Using the derived formulas, we present an example calibration to market data. Journal: Applied Mathematical Finance Pages: 281-301 Issue: 4 Volume: 24 Year: 2017 Month: 7 X-DOI: 10.1080/1350486X.2017.1378582 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1378582 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:4:p:281-301 Template-Type: ReDIF-Article 1.0 Author-Name: S. N. Singor Author-X-Name-First: S. N. Author-X-Name-Last: Singor Author-Name: A. Boer Author-X-Name-First: A. Author-X-Name-Last: Boer Author-Name: J. S. C. Alberts Author-X-Name-First: J. S. C. Author-X-Name-Last: Alberts Author-Name: C. W. Oosterlee Author-X-Name-First: C. W. Author-X-Name-Last: Oosterlee Title: On the modelling of nested risk-neutral stochastic processes with applications in insurance Abstract: We propose a modelling framework for risk-neutral stochastic processes nested in a real-world stochastic process. The framework is important for insurers that deal with the valuation of embedded options and in particular at future points in time. We make use of the class of State Space Hidden Markov models for modelling the joint behaviour of the parameters of a risk-neutral model and the dynamics of option market instruments. This modelling concept enables us to perform non-linear estimation, forecasting and robust calibration. The proposed method is applied to the Heston model for which we find highly satisfactory results. We use the estimated Heston model to compute the required capital of an insurance company under Solvency II and we find large differences compared to a basic calibration method. Journal: Applied Mathematical Finance Pages: 302-336 Issue: 4 Volume: 24 Year: 2017 Month: 7 X-DOI: 10.1080/1350486X.2017.1378583 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1378583 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:4:p:302-336 Template-Type: ReDIF-Article 1.0 Author-Name: J. Lars Kirkby Author-X-Name-First: J. Lars Author-X-Name-Last: Kirkby Title: Robust barrier option pricing by frame projection under exponential Lévy dynamics Abstract: We present an efficient method for robustly pricing discretely monitored barrier and occupation time derivatives under exponential Lévy models. This includes ordinary barrier options, as well as (resetting) Parisian options, delayed barrier options (also known as cumulative Parisian or Parasian options), fader options and step options (soft-barriers), all with single and double barriers, which have yet to be priced with more general Lévy processes, including KoBoL (CGMY), Merton’s jump diffusion and NIG. The method’s efficiency is derived in part from the use of frame-projected transition densities, which transform the problem into the Fourier domain and accelerate the convergence of intermediate expectations. Moreover, these expectations are approximated by Toeplitz matrix-vector multiplications, resulting in a fast implementation. We devise an augmentation approach that contributes to the method’s robustness, adding protection against mis-specifying a proper truncation support of the transition density. Theoretical convergence is verified by a series of numerical experiments which demonstrate the method’s efficiency and accuracy. Journal: Applied Mathematical Finance Pages: 337-386 Issue: 4 Volume: 24 Year: 2017 Month: 7 X-DOI: 10.1080/1350486X.2017.1384701 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1384701 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:4:p:337-386 Template-Type: ReDIF-Article 1.0 Author-Name: Peter A. Forsyth Author-X-Name-First: Peter A. Author-X-Name-Last: Forsyth Author-Name: Kenneth R. Vetzal Author-X-Name-First: Kenneth R. Author-X-Name-Last: Vetzal Title: Optimal Asset Allocation for Retirement Saving: Deterministic Vs. Time Consistent Adaptive Strategies Abstract: We consider optimal asset allocation for an investor saving for retirement. The portfolio contains a bond index and a stock index. We use multi-period criteria and explore two types of strategies: deterministic strategies are based only on the time remaining until the anticipated retirement date, while adaptive strategies also consider the investor’s accumulated wealth. The vast majority of financial products designed for retirement saving use deterministic strategies (e.g., target date funds). In the deterministic case, we determine an optimal open loop control using mean-variance criteria. In the adaptive case, we use time consistent mean-variance and quadratic shortfall objectives. Tests based on both a synthetic market where the stock index is modelled by a jump-diffusion process and also on bootstrap resampling of long-term historical data show that the optimal adaptive strategies significantly outperform the optimal deterministic strategy. This suggests that investors are not being well served by the strategies currently dominating the marketplace. Journal: Applied Mathematical Finance Pages: 1-37 Issue: 1 Volume: 26 Year: 2019 Month: 1 X-DOI: 10.1080/1350486X.2019.1584534 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1584534 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:1:p:1-37 Template-Type: ReDIF-Article 1.0 Author-Name: Matthew Lorig Author-X-Name-First: Matthew Author-X-Name-Last: Lorig Author-Name: Zhou Zhou Author-X-Name-First: Zhou Author-X-Name-Last: Zhou Author-Name: Bin Zou Author-X-Name-First: Bin Author-X-Name-Last: Zou Title: A Mathematical Analysis of Technical Analysis Abstract: In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modelled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to investigate how the performance of optimal ExpMA strategies is affected by variations in model parameters and by transaction costs. Journal: Applied Mathematical Finance Pages: 38-68 Issue: 1 Volume: 26 Year: 2019 Month: 1 X-DOI: 10.1080/1350486X.2019.1588136 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1588136 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:1:p:38-68 Template-Type: ReDIF-Article 1.0 Author-Name: Peng Yaohao Author-X-Name-First: Peng Author-X-Name-Last: Yaohao Author-Name: Pedro Henrique Melo Albuquerque Author-X-Name-First: Pedro Henrique Melo Author-X-Name-Last: Albuquerque Title: Non-Linear Interactions and Exchange Rate Prediction: Empirical Evidence Using Support Vector Regression Abstract: This paper analysed the prediction of the spot exchange rate of 10 currency pairs using support vector regression (SVR) based on a fundamentalist model composed of 13 explanatory variables. Different structures of non-linear dependence introduced by nine different Kernel functions were tested and the predictions were compared to the Random Walk benchmark. We checked the explanatory power gain of SVR models over the Random Walk by applying White’s Reality Check Test. The results showed that the majority of SVR models achieved better out-of-sample performance than the Random Walk, but in overall they failed to achieve statistical significance of predictive superiority. Furthermore, we observed that non-mainstream Kernel functions performed better than the ones commonly used in the machine-learning literature, a finding that can provide new insights regarding machine-learning methods applications and the predictability of exchange rates using non-linear interactions between the predictors. Journal: Applied Mathematical Finance Pages: 69-100 Issue: 1 Volume: 26 Year: 2019 Month: 1 X-DOI: 10.1080/1350486X.2019.1593866 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1593866 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:1:p:69-100 Template-Type: ReDIF-Article 1.0 Author-Name: Hua-Yi Lin Author-X-Name-First: Hua-Yi Author-X-Name-Last: Lin Author-Name: Arash Fahim Author-X-Name-First: Arash Author-X-Name-Last: Fahim Title: Optimal portfolio execution under time-varying liquidity constraints Abstract: In this article, we take an algorithmic approach to solve the problem of optimal execution under time-varying constraints on the depth of a limit order book (LOB). Our algorithms are within the resilience model proposed by Obizhaeva and Wang (2013) with a more realistic assumption on the order book depth; the amount of liquidity provided by an LOB market is finite at all times. For the simplest case where the order book depth stays at a fixed level for the entire trading horizon, we reduce the optimal execution problem into a one-dimensional root-finding problem which can be readily solved by standard numerical algorithms. When the depth of the order book is monotone in time, we apply the Karush-Kuhn-Tucker conditions to narrow down the set of candidate strategies. Then, we use a dichotomy-based search algorithm to pin down the optimal one. For the general case, we start from the optimal strategy subject to no liquidity constraints and iterate over execution strategy by sequentially adding more constraints to the problem in a specific fashion until primal feasibility is achieved. Numerical experiments indicate that our algorithms give comparable results to those of current existing convex optimization toolbox CVXOPT with significantly lower time complexity. Journal: Applied Mathematical Finance Pages: 387-416 Issue: 5 Volume: 24 Year: 2017 Month: 9 X-DOI: 10.1080/1350486X.2017.1405731 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1405731 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:5:p:387-416 Template-Type: ReDIF-Article 1.0 Author-Name: Florian Klöck Author-X-Name-First: Florian Author-X-Name-Last: Klöck Author-Name: Alexander Schied Author-X-Name-First: Alexander Author-X-Name-Last: Schied Author-Name: Yuemeng Sun Author-X-Name-First: Yuemeng Author-X-Name-Last: Sun Title: Price manipulation in a market impact model with dark pool Abstract: For a market impact model, price manipulation and related notions play a role that is similar to the role of arbitrage in a derivatives pricing model. Here, we give a systematic investigation into such regularity issues when orders can be executed both at a traditional exchange and in a dark pool. To this end, we focus on a class of dark-pool models whose market impact at the exchange is described by an Almgren–Chriss model. Conditions for the absence of price manipulation for all Almgren–Chriss models include the absence of temporary cross-venue impact, the presence of full permanent cross-venue impact and the additional penalization of orders executed in the dark pool. When a particular Almgren–Chriss model has been fixed, we show by a number of examples that the regularity of the dark-pool model hinges in a subtle way on the interplay of all model parameters and on the liquidation time constraint. The paper can also be seen as a case study for the regularity of market impact models in general. Journal: Applied Mathematical Finance Pages: 417-450 Issue: 5 Volume: 24 Year: 2017 Month: 9 X-DOI: 10.1080/1350486X.2017.1406438 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1406438 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:5:p:417-450 Template-Type: ReDIF-Article 1.0 Author-Name: Oliver Janke Author-X-Name-First: Oliver Author-X-Name-Last: Janke Title: Utility maximization under risk constraints and incomplete information for a market with a change point Abstract: In this article, we consider an optimization problem of expected utility maximization of continuous-time trading in a financial market. This trading is constrained by a benchmark for a utility-based shortfall risk measure. The market consists of one asset whose price process is modelled by a Geometric Brownian motion where the market parameters change at a random time. The information flow is modelled by initially and progressively enlarged filtrations which represent the knowledge about the price process, the Brownian motion and the random time. We solve the maximization problem and give the optimal terminal wealth depending on these different filtrations for general utility functions by using martingale representation results for the corresponding filtration. Journal: Applied Mathematical Finance Pages: 451-484 Issue: 5 Volume: 24 Year: 2017 Month: 9 X-DOI: 10.1080/1350486X.2017.1409080 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1409080 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:5:p:451-484 Template-Type: ReDIF-Article 1.0 Author-Name: Dan Pirjol Author-X-Name-First: Dan Author-X-Name-Last: Pirjol Author-Name: Jing Wang Author-X-Name-First: Jing Author-X-Name-Last: Wang Author-Name: Lingjiong Zhu Author-X-Name-First: Lingjiong Author-X-Name-Last: Zhu Title: Short Maturity Forward Start Asian Options in Local Volatility Models Abstract: We study the short maturity asymptotics for prices of forward start Asian options under the assumption that the underlying asset follows a local volatility model. We obtain asymptotics for the cases of out-of-the-money, in-the-money, and at-the-money, considering both fixed strike and floating Asian options. The exponential decay of the price of an out-of-the-money forward start Asian option is handled using large deviations theory, and is controlled by a rate function which is given by a double-layer optimization problem. In the Black-Scholes model, the calculation of the rate function is simplified further to the solution of a non-linear equation. We obtain closed form for the rate function, as well as its asymptotic behavior when the strike is extremely large, small, or close to the initial price of the underlying asset. Journal: Applied Mathematical Finance Pages: 187-221 Issue: 3 Volume: 26 Year: 2019 Month: 5 X-DOI: 10.1080/1350486X.2019.1584533 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1584533 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:3:p:187-221 Template-Type: ReDIF-Article 1.0 Author-Name: Géraldine Bouveret Author-X-Name-First: Géraldine Author-X-Name-Last: Bouveret Title: Dual Representation of the Cost of Designing a Portfolio Satisfying Multiple Risk Constraints Abstract: We consider, within a Markovian complete financial market, the problem of finding the least expensive portfolio process meeting, at each payment date, three different types of risk criterion. Two of them encompass an expected utility-based measure and a quantile hedging constraint imposed at inception on all the future payment dates, while the other one is a quantile hedging constraint set at each payment date over the next one. The quantile risk measures are defined with respect to a stochastic benchmark and the expected utility-based constraint is applied to random payment dates. We explicit the Legendre-Fenchel transform of the pricing function. We also provide, for each quantile hedging problem, a backward dual algorithm allowing to compute their associated value function by backward recursion. The algorithms are illustrated with a numerical example. Journal: Applied Mathematical Finance Pages: 222-256 Issue: 3 Volume: 26 Year: 2019 Month: 5 X-DOI: 10.1080/1350486X.2019.1638276 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1638276 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:3:p:222-256 Template-Type: ReDIF-Article 1.0 Author-Name: Syoiti Ninomiya Author-X-Name-First: Syoiti Author-X-Name-Last: Ninomiya Author-Name: Yuji Shinozaki Author-X-Name-First: Yuji Author-X-Name-Last: Shinozaki Title: Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing Abstract: This study proposes new higher-order discretization methods of forward-backward stochastic differential equations. In the proposed methods, the forward component is discretized using the Kusuoka–Lyons–Ninomiya–Victoir scheme with discrete random variables and the backward component using a higher-order numerical integration method consistent with the discretization method of the forward component, by use of the tree based branching algorithm. The proposed methods are applied to the XVA pricing, in particular to the credit valuation adjustment. The numerical results show that the expected theoretical order and computational efficiency could be achieved. Journal: Applied Mathematical Finance Pages: 257-292 Issue: 3 Volume: 26 Year: 2019 Month: 5 X-DOI: 10.1080/1350486X.2019.1637268 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1637268 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:3:p:257-292 Template-Type: ReDIF-Article 1.0 Author-Name: Patrik Karlsson Author-X-Name-First: Patrik Author-X-Name-Last: Karlsson Author-Name: Shashi Jain Author-X-Name-First: Shashi Author-X-Name-Last: Jain Author-Name: Cornelis W. Oosterlee Author-X-Name-First: Cornelis W. Author-X-Name-Last: Oosterlee Title: Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method Abstract: The regulatory credit value adjustment (CVA) for an outstanding over-the-counter (OTC) derivative portfolio is computed based on the portfolio exposure over its lifetime. Usually, the future portfolio exposure is approximated using the Monte Carlo simulation, as the portfolio value can be driven by several market risk-factors. For derivatives, such as Bermudan swaptions, that do not have an analytical approximation for their Mark-to-Market (MtM) value, the standard market practice is to use the regression functions from the least squares Monte Carlo method to approximate their MtM along simulated scenarios. However, such approximations have significant bias and noise, resulting in inaccurate CVA charge. In this paper, we extend the Stochastic Grid Bundling Method (SGBM) for the one-factor Gaussian short rate model, to efficiently and accurately compute Expected Exposure, Potential Future exposure and CVA for Bermudan swaptions. A novel contribution of the paper is that it demonstrates how different measures, for instance spot and terminal measure, can simultaneously be employed in the SGBM framework, to significantly reduce the variance and bias of the solution. Journal: Applied Mathematical Finance Pages: 175-196 Issue: 3 Volume: 23 Year: 2016 Month: 5 X-DOI: 10.1080/1350486X.2016.1226144 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1226144 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:3:p:175-196 Template-Type: ReDIF-Article 1.0 Author-Name: Clément Ménassé Author-X-Name-First: Clément Author-X-Name-Last: Ménassé Author-Name: Peter Tankov Author-X-Name-First: Peter Author-X-Name-Last: Tankov Title: Approximate indifference pricing in exponential Lévy models Abstract: Financial markets based on Lévy processes are typically incomplete and option prices depend on risk attitudes of individual agents. In this context, the notion of utility indifference price has gained popularity in the academic circles. Although theoretically very appealing, this pricing method remains difficult to apply in practice, due to the high computational cost of solving the non-linear partial integro-differential equation associated to the indifference price. In this work, we develop closed-form approximations to exponential utility indifference prices in exponential Lévy models. To this end, we first establish a new non-asymptotic approximation of the indifference price which extends earlier results on small risk aversion asymptotics of this quantity. Next, we use this formula to derive a closed-form approximation of the indifference price by treating the Lévy model as a perturbation of the Black–Scholes model. This extends the methodology introduced in a recent paper for smooth linear functionals of Lévy processes (Černý et al. 2013) to non-linear and non-smooth functionals. Our formula represents the indifference price as the linear combination of the Black–Scholes price and correction terms which depend on the variance, skewness and kurtosis of the underlying Lévy process, and the derivatives of the Black–Scholes price. As a by-product, we obtain a simple approximation for the spread between the buyer’s and the seller’s indifference price. This formula allows to quantify, in a model-independent fashion, how sensitive a given product is to jump risk when jump size is small. Journal: Applied Mathematical Finance Pages: 197-235 Issue: 3 Volume: 23 Year: 2016 Month: 5 X-DOI: 10.1080/1350486X.2016.1227270 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1227270 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:3:p:197-235 Template-Type: ReDIF-Article 1.0 Author-Name: Ernst Eberlein Author-X-Name-First: Ernst Author-X-Name-Last: Eberlein Author-Name: M’hamed Eddahbi Author-X-Name-First: M’hamed Author-X-Name-Last: Eddahbi Author-Name: S. M. Lalaoui Ben Cherif Author-X-Name-First: S. M. Author-X-Name-Last: Lalaoui Ben Cherif Title: Computation of Greeks in LIBOR models driven by time–inhomogeneous Lévy processes Abstract: The aim of this article is to compute Greeks, i.e. price sensitivities in the framework of the Lévy LIBOR model. Two approaches are discussed. The first approach is based on the integration-by-parts formula, which lies at the core of the application of the Malliavin calculus to finance. The second approach consists of using Fourier-based methods for pricing derivatives. We illustrate the result by applying the formula to a caplet price where the jump part of the driving process of the underlying model is given by a time–inhomogeneous Gamma process and alternatively by a Variance Gamma process. Journal: Applied Mathematical Finance Pages: 236-260 Issue: 3 Volume: 23 Year: 2016 Month: 5 X-DOI: 10.1080/1350486X.2016.1243013 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1243013 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:3:p:236-260 Template-Type: ReDIF-Article 1.0 Author-Name: Andrey Itkin Author-X-Name-First: Andrey Author-X-Name-Last: Itkin Title: Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps Abstract: It is known that the implied volatility skew of Forex (FX) options demonstrates a stochastic behaviour which is called stochastic skew. In this paper, we create stochastic skew by assuming the spot/instantaneous variance (InV) correlation to be stochastic. Accordingly, we consider a class of Stochastic Local Volatility (SLV) models with stochastic correlation where all drivers – the spot, InV and their correlation – are modelled by processes. We assume all diffusion components to be fully correlated, as well as all jump components. A new fully implicit splitting finite-difference scheme is proposed for solving forward PIDE which is used when calibrating the model to market prices of the FX options with different strikes and maturities. The scheme is unconditionally stable, of second order of approximation in time and space, and achieves a linear complexity in each spatial direction. The results of simulation obtained by using this model demonstrate the capacity of the presented approach in modelling stochastic skew. Journal: Applied Mathematical Finance Pages: 485-519 Issue: 6 Volume: 24 Year: 2017 Month: 11 X-DOI: 10.1080/1350486X.2017.1409641 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1409641 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:6:p:485-519 Template-Type: ReDIF-Article 1.0 Author-Name: Barbara Goetz Author-X-Name-First: Barbara Author-X-Name-Last: Goetz Author-Name: Marcos Escobar Author-X-Name-First: Marcos Author-X-Name-Last: Escobar Author-Name: Rudi Zagst Author-X-Name-First: Rudi Author-X-Name-Last: Zagst Title: Two asset-barrier option under stochastic volatility Abstract: Financial products which depend on hitting times for two underlying assets have become very popular in the last decade. Three common examples are double-digital barrier options, two-asset barrier spread options and double lookback options. Analytical expressions for the joint distribution of the endpoints and the maximum and/or minimum values of two assets are essential in order to obtain quasi-closed form solutions for the price of these derivatives. Earlier authors derived quasi-closed form pricing expressions in the context of constant volatility and correlation. More recently solutions were provided in the presence of a common stochastic volatility factor but with restricted correlations due to the use of a method of images. In this article, we generalize this finding by allowing any value for the correlation. In this context, we derive closed-form expressions for some two-asset barrier options. Journal: Applied Mathematical Finance Pages: 520-546 Issue: 6 Volume: 24 Year: 2017 Month: 11 X-DOI: 10.1080/1350486X.2017.1419910 File-URL: http://hdl.handle.net/10.1080/1350486X.2017.1419910 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:6:p:520-546 Template-Type: ReDIF-Article 1.0 Author-Name: José E. Figueroa-López Author-X-Name-First: José E. Author-X-Name-Last: Figueroa-López Author-Name: Ruoting Gong Author-X-Name-First: Ruoting Author-X-Name-Last: Gong Author-Name: Christian Houdré Author-X-Name-First: Christian Author-X-Name-Last: Houdré Title: Third-order short-time expansions for close-to-the-money option prices under the CGMY model Abstract: A third-order approximation for close-to-the-money European option prices under an infinite-variation CGMY Lévy model is derived, and is then extended to a model with an additional independent Brownian component. The asymptotic regime considered, in which the strike is made to converge to the spot stock price as the maturity approaches zero, is relevant in applications since the most liquid options have strikes that are close to the spot price. Our results shed new light on the connection between both the volatility of the continuous component and the jump parameters and the behaviour of option prices near expiration when the strike is close to the spot price. In particular, a new type of transition phenomenon is uncovered in which the third-order term exhibits two distinct asymptotic regimes depending on whether $$Y \in (1,3/2)$$Y∈(1,3/2) or $$Y \in (3/2,2)$$Y∈(3/2,2) . Unlike second-order approximations, the expansions herein are shown to be remarkably accurate so that they can actually be used for calibrating some model parameters. For illustration, we calibrate the volatility $$\sigma $$σ of the Brownian component and the jump intensity C of the CGMY model to actual option prices. Journal: Applied Mathematical Finance Pages: 547-574 Issue: 6 Volume: 24 Year: 2017 Month: 11 X-DOI: 10.1080/1350486X.2018.1429935 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1429935 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:24:y:2017:i:6:p:547-574 Template-Type: ReDIF-Article 1.0 Author-Name: Sergei Levendorskiĭ Author-X-Name-First: Sergei Author-X-Name-Last: Levendorskiĭ Title: Pitfalls of the Fourier Transform Method in Affine Models, and Remedies Abstract: We study sources of potentially serious errors of popular numerical realizations of the Fourier method in affine models and explain that, in many cases, a calibration procedure based on such a realization will be able to find a “correct parameter set” only in a rather small region of the parameter space, with a blind spot: an interval of strikes depending on the model and time to maturity, where accurate calculations are extremely time-consuming. We explain how to construct more accurate and faster pricing and calibration procedures. An important ingredient of our method is the study of the analytic continuation of the solution of the associated system of generalized Riccati equations, and contour deformation techniques. As a byproduct, we show that the straightforward application of the Runge–Kutta method may lead to sizable errors, and suggest certain remedies. In the paper, the method is applied to a wide class of stochastic volatility models with stochastic interest rate and interest rate models of An(n) class. The methodology of the paper can be applied to other models (e.g., quadratic term structure models, Wishart dynamics, 3/2-model). Journal: Applied Mathematical Finance Pages: 81-134 Issue: 2 Volume: 23 Year: 2016 Month: 3 X-DOI: 10.1080/1350486X.2016.1159918 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1159918 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:2:p:81-134 Template-Type: ReDIF-Article 1.0 Author-Name: Stefan Gerhold Author-X-Name-First: Stefan Author-X-Name-Last: Gerhold Author-Name: I. Cetin Gülüm Author-X-Name-First: I. Cetin Author-X-Name-Last: Gülüm Author-Name: Arpad Pinter Author-X-Name-First: Arpad Author-X-Name-Last: Pinter Title: Small-Maturity Asymptotics for the At-The-Money Implied Volatility Slope in Lévy Models Abstract: We consider the at-the-money (ATM) strike derivative of implied volatility as the maturity tends to zero. Our main results quantify the behaviour of the slope for infinite activity exponential Lévy models including a Brownian component. As auxiliary results, we obtain asymptotic expansions of short maturity ATM digital call options, using Mellin transform asymptotics. Finally, we discuss when the ATM slope is consistent with the steepness of the smile wings, as given by Lee’s moment formula. Journal: Applied Mathematical Finance Pages: 135-157 Issue: 2 Volume: 23 Year: 2016 Month: 3 X-DOI: 10.1080/1350486X.2016.1197041 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1197041 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:2:p:135-157 Template-Type: ReDIF-Article 1.0 Author-Name: Ludger Rüschendorf Author-X-Name-First: Ludger Author-X-Name-Last: Rüschendorf Author-Name: Viktor Wolf Author-X-Name-First: Viktor Author-X-Name-Last: Wolf Title: On the Method of Optimal Portfolio Choice by Cost-Efficiency Abstract: We develop the method of optimal portfolio choice based on the concept of cost-efficiency in two directions. First, instead of specifying a payoff distribution in an unique way, we allow customer-defined constraints and preferences for the choice of a distributional form of the payoff distribution. This leads to a class of possible payoff distributions. We determine upper and lower bounds for the corresponding strategies in stochastic order and describe related upper and lower price bounds for the induced class of cost-efficient payoffs. While the results for the cost-efficient payoff given so far in the literature in the context of Lévy models are based on the Esscher pricing measure we use as alternative the method of empirical pricing measures. This method is well established in the literature and leads to more precise pricing of options and their cost-efficient counterparts. We show in some examples for real market data that this choice is numerically feasible and leads to more precise prices for the cost-efficient payoffs and for values of the efficiency loss. Journal: Applied Mathematical Finance Pages: 158-173 Issue: 2 Volume: 23 Year: 2016 Month: 3 X-DOI: 10.1080/1350486X.2016.1204238 File-URL: http://hdl.handle.net/10.1080/1350486X.2016.1204238 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:23:y:2016:i:2:p:158-173 Template-Type: ReDIF-Article 1.0 Author-Name: Ramin Okhrati Author-X-Name-First: Ramin Author-X-Name-Last: Okhrati Title: Hedging the Risk of Delayed Data in Defaultable Markets Abstract: We investigate hedging the risk of delayed data in certain defaultable securities through the local risk minimization approach. From a financial point of view, this indicates that in addition to the risk of default, investors also face incomplete accounting data. In our analysis, the delay is modelled by a random time change, and different levels of information, including the full market’s, management’s, and investors’ information, are distinguished. We obtain semi-explicit solutions for pseudo locally risk minimizing hedging strategies from the perspective of investors where the results are presented according to the solutions of partial differential equations. In obtaining the main results of this paper, we apply a filtration expansion theorem that determines the canonical decomposition of stopped special semimartingales in an enlarged filtration of investors’ information. Journal: Applied Mathematical Finance Pages: 101-130 Issue: 2 Volume: 26 Year: 2019 Month: 3 X-DOI: 10.1080/1350486X.2019.1590784 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1590784 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:2:p:101-130 Template-Type: ReDIF-Article 1.0 Author-Name: Jimin Lin Author-X-Name-First: Jimin Author-X-Name-Last: Lin Author-Name: Matthew Lorig Author-X-Name-First: Matthew Author-X-Name-Last: Lorig Title: On Carr and Lee’s Correlation Immunization Strategy Abstract: In their seminal work Robust Replication of Volatility Derivatives, Carr and Lee show how to robustly price and replicate a variety of claims written on the quadratic variation of a risky asset under the assumption that the asset’s volatility process is independent of the Brownian motion that drives the asset’s price. Additionally, they propose a correlation immunization strategy that minimizes the pricing and hedging error that results when the correlation between the risky asset’s price and volatility is non-zero. In this paper, we show that the correlation immunization strategy is the only strategy among the class of strategies discussed in Carr and Lee's paper that results in real-valued hedging portfolios when the correlation between the asset’s price and volatility is non-zero. Additionally, we perform a number of Monte Carlo experiments to test the effectiveness of Carr and Lee’s immunization strategy. Our results indicate that the correlation immunization method is an effective means of reducing pricing and hedging errors that result from a non-zero correlation. Journal: Applied Mathematical Finance Pages: 131-152 Issue: 2 Volume: 26 Year: 2019 Month: 3 X-DOI: 10.1080/1350486X.2019.1598276 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1598276 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:2:p:131-152 Template-Type: ReDIF-Article 1.0 Author-Name: Xuancheng Huang Author-X-Name-First: Xuancheng Author-X-Name-Last: Huang Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Author-Name: Mojtaba Nourian Author-X-Name-First: Mojtaba Author-X-Name-Last: Nourian Title: Mean-Field Game Strategies for Optimal Execution Abstract: Algorithmic trading strategies for execution often focus on the individual agent who is liquidating/acquiring shares. When generalized to multiple agents, the resulting stochastic game is notoriously difficult to solve in closed-form. Here, we circumvent the difficulties by investigating a mean-field game framework containing (i) a major agent who is liquidating a large number of shares, (ii) a number of minor agents (high-frequency traders (HFTs)) who detect and trade against the liquidator, and (iii) noise traders who buy and sell for exogenous reasons. Our setup accounts for permanent price impact stemming from all trader types inducing an interaction between major and minor agents. Both optimizing agents trade against noise traders as well as one another. This stochastic dynamic game contains couplings in the price and trade dynamics, and we use a mean-field game approach to solve the problem. We obtain a set of decentralized feedback trading strategies for the major and minor agents, and express the solution explicitly in terms of a deterministic fixed point problem. For a finite $$N$$N population of HFTs, the set of major-minor agent mean-field game strategies is shown to have a $${{\epsilon}_N}$$ϵN -Nash equilibrium property where $${{\epsilon}_N} \to 0$$ϵN→0 as $$N \to \infty $$N→∞ . Journal: Applied Mathematical Finance Pages: 153-185 Issue: 2 Volume: 26 Year: 2019 Month: 3 X-DOI: 10.1080/1350486X.2019.1603183 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1603183 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:2:p:153-185 Template-Type: ReDIF-Article 1.0 Author-Name: Olivier Guéant Author-X-Name-First: Olivier Author-X-Name-Last: Guéant Author-Name: Iuliia Manziuk Author-X-Name-First: Iuliia Author-X-Name-Last: Manziuk Title: Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality Abstract: In corporate bond markets, which are mainly OTC markets, market makers play a central role by providing bid and ask prices for bonds to asset managers. Determining the optimal bid and ask quotes that a market maker should set for a given universe of bonds is a complex task. The existing models, mostly inspired by the Avellaneda-Stoikov model, describe the complex optimization problem faced by market makers: proposing bid and ask prices for making money out of the difference between them while mitigating the market risk associated with holding inventory. While most of the models only tackle one-asset market making, they can often be generalized to a multi-asset framework. However, the problem of solving the equations characterizing the optimal bid and ask quotes numerically is seldom tackled in the literature, especially in high dimension. In this paper, we propose a numerical method for approximating the optimal bid and ask quotes over a large universe of bonds in a model à la Avellaneda–Stoikov. As classical finite difference methods cannot be used in high dimension, we present a discrete-time method inspired by reinforcement learning techniques, namely, a model-based deep actor-critic algorithm. Journal: Applied Mathematical Finance Pages: 387-452 Issue: 5 Volume: 26 Year: 2019 Month: 9 X-DOI: 10.1080/1350486X.2020.1714455 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1714455 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:5:p:387-452 Template-Type: ReDIF-Article 1.0 Author-Name: Tony Ware Author-X-Name-First: Tony Author-X-Name-Last: Ware Title: Polynomial Processes for Power Prices Abstract: Polynomial processes have the property that expectations of polynomial functions (of degree n, say) of the future state of the process conditional on the current state are given by polynomials (of degree ≤ n) of the current state. Here we explore the potential of polynomial maps of polynomial processes for modelling energy prices. We focus on the example of Alberta power prices, derive one- and two-factor models for spot prices. We examine their performance in numerical experiments, and demonstrate that the richness of the dynamics they are able to generate makes them well suited for modelling even extreme examples of energy price behaviour. Journal: Applied Mathematical Finance Pages: 453-474 Issue: 5 Volume: 26 Year: 2019 Month: 9 X-DOI: 10.1080/1350486X.2020.1715808 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1715808 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:5:p:453-474 Template-Type: ReDIF-Article 1.0 Author-Name: Cord Harms Author-X-Name-First: Cord Author-X-Name-Last: Harms Author-Name: Rüdiger Kiesel Author-X-Name-First: Rüdiger Author-X-Name-Last: Kiesel Title: Structural Electricity Models and Asymptotically Normal Estimators to Quantify Parameter Risk Abstract: We estimate a structural electricity (multi-commodity) model based on historical spot and futures data (fuels and power prices, respectively) and quantify the inherent parameter risk using an average value at risk approach (‘expected shortfall’). The mathematical proofs use the theory of asymptotic statistics to derive a parameter risk measure. We use far in-the-money options to derive a confidence level and use it as a prudent present value adjustment when pricing a virtual power plant. Finally, we conduct a present value benchmarking to compare the approach of temperature-driven demand (based on load data) to an ‘implied demand approach’ (demand implied from observable power futures prices). We observe that the implied demand approach can easily capture observed electricity price volatility whereas the estimation against observable load data will lead to a gap, because – amongst others – the interplay of demand and supply is not captured in the data (i.e., unexpected mismatches). Journal: Applied Mathematical Finance Pages: 475-522 Issue: 5 Volume: 26 Year: 2019 Month: 9 X-DOI: 10.1080/1350486X.2020.1725582 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1725582 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:5:p:475-522 Template-Type: ReDIF-Article 1.0 Author-Name: Konstantinos Spiliopoulos Author-X-Name-First: Konstantinos Author-X-Name-Last: Spiliopoulos Author-Name: Jia Yang Author-X-Name-First: Jia Author-X-Name-Last: Yang Title: Network Effects in Default Clustering for Large Systems Abstract: We consider a large collection of dynamically interacting components defined on a weighted-directed graph determining the impact of the default of one component to another one. We prove a law of large numbers for the empirical measure capturing the evolution of the different components in the pool and from this we extract important information for quantities such as the loss rate in the overall pool as well as the mean impact on a given component from system-wide defaults. A singular value decomposition of the adjacency matrix of the graph allows to coarse-grain the system by focusing on the highest eigenvalues which also correspond to the components with the highest contagion impact on the pool. Numerical simulations demonstrate the theoretical findings. Journal: Applied Mathematical Finance Pages: 523-582 Issue: 6 Volume: 26 Year: 2019 Month: 11 X-DOI: 10.1080/1350486X.2020.1724804 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1724804 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:6:p:523-582 Template-Type: ReDIF-Article 1.0 Author-Name: Terry Lyons Author-X-Name-First: Terry Author-X-Name-Last: Lyons Author-Name: Sina Nejad Author-X-Name-First: Sina Author-X-Name-Last: Nejad Author-Name: Imanol Perez Arribas Author-X-Name-First: Imanol Author-X-Name-Last: Perez Arribas Title: Numerical Method for Model-free Pricing of Exotic Derivatives in Discrete Time Using Rough Path Signatures Abstract: We estimate prices of exotic options in a discrete-time model-free setting when the trader has access to market prices of a rich enough class of exotic and vanilla options. This is achieved by estimating an unobservable quantity called ‘implied expected signature’ from such market prices, which are used to price other exotic derivatives. The implied expected signature is an object that characterizes the market dynamics. Journal: Applied Mathematical Finance Pages: 583-597 Issue: 6 Volume: 26 Year: 2019 Month: 11 X-DOI: 10.1080/1350486X.2020.1726784 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1726784 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:6:p:583-597 Template-Type: ReDIF-Article 1.0 Author-Name: Jan-Frederik Mai Author-X-Name-First: Jan-Frederik Author-X-Name-Last: Mai Title: Portfolio Optimization for Credit-Risky Assets under Marshall–Olkin Dependence Abstract: We consider power/logarithmic utility maximization in a multivariate Black–Scholes model that is enhanced by credit risk via the Marshall–Olkin exponential distribution. On the practical side, the model results in an enhancement of the mean variance paradigm, which is easy to interpret and implement. On the theoretical side, the model constitutes a well-justified and intuitive mathematical wrapping to study the effect of extreme and higher-order dependence on optimal portfolios. Journal: Applied Mathematical Finance Pages: 598-618 Issue: 6 Volume: 26 Year: 2019 Month: 11 X-DOI: 10.1080/1350486X.2020.1727755 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1727755 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:26:y:2019:i:6:p:598-618 Template-Type: ReDIF-Article 1.0 Author-Name: Luciano Campi Author-X-Name-First: Luciano Author-X-Name-Last: Campi Author-Name: Diego Zabaljauregui Author-X-Name-First: Diego Author-X-Name-Last: Zabaljauregui Title: Optimal Market Making under Partial Information with General Intensities Abstract: Starting from the Avellaneda–Stoikov framework, we consider a market maker who wants to optimally set bid/ask quotes over a finite time horizon, to maximize her expected utility. The intensities of the orders she receives depend not only on the spreads she quotes but also on unobservable factors modelled by a hidden Markov chain. We tackle this stochastic control problem under partial information with a model that unifies and generalizes many existing ones under full information, combining several risk metrics and constraints, and using general decreasing intensity functionals. We use stochastic filtering, control and piecewise-deterministic Markov processes theory, to reduce the dimensionality of the problem and characterize the reduced value function as the unique continuous viscosity solution of its dynamic programming equation. We then solve the analogous full information problem and compare the results numerically through a concrete example. We show that the optimal full information spreads are biased when the exact market regime is unknown, and the market maker needs to adjust for additional regime uncertainty in terms of P&L sensitivity and observed order flow volatility. This effect becomes higher, the longer the waiting time in between orders. Journal: Applied Mathematical Finance Pages: 1-45 Issue: 1-2 Volume: 27 Year: 2020 Month: 7 X-DOI: 10.1080/1350486X.2020.1758587 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1758587 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:1-2:p:1-45 Template-Type: ReDIF-Article 1.0 Author-Name: Lina von Sydow Author-X-Name-First: Lina Author-X-Name-Last: von Sydow Author-Name: Johan Walden Author-X-Name-First: Johan Author-X-Name-Last: Walden Title: Numerical Ross Recovery for Diffusion Processes Using a PDE Approach Abstract: We develop and analyse a numerical method for solving the Ross recovery problem for a diffusion problem with unbounded support, with a transition independent pricing kernel. Asset prices are assumed to only be available on a bounded subinterval $$B = [- N,N]$$B=[−N,N]. Theoretical error bounds on the recovered pricing kernel are derived, relating the convergence rate as a function of $$N$$N to the rate of mean reversion of the diffusion process. Our suggested numerical method for finding the pricing kernel employs finite differences, and we apply Sturm–Liouville theory to make use of inverse iteration on the resulting discretized eigenvalue problem. We numerically verify the derived error bounds on a test bench of three model problems. Journal: Applied Mathematical Finance Pages: 46-66 Issue: 1-2 Volume: 27 Year: 2020 Month: 7 X-DOI: 10.1080/1350486X.2020.1730202 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1730202 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:1-2:p:46-66 Template-Type: ReDIF-Article 1.0 Author-Name: Álvaro Cartea Author-X-Name-First: Álvaro Author-X-Name-Last: Cartea Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Author-Name: Yixuan Wang Author-X-Name-First: Yixuan Author-X-Name-Last: Wang Title: Spoofing and Price Manipulation in Order-Driven Markets Abstract: We model the trading strategy of an investor who spoofs the limit order book (LOB) to increase the revenue obtained from selling a position in a security. The strategy employs, in addition to sell limit orders (LOs) and sell market orders (MOs), a large number of spoof buy LOs to manipulate the volume imbalance of the LOB. Spoofing is illegal, so the strategy trades off the gains that originate from spoofing against the expected financial losses due to a fine imposed by the financial authorities. As the fine increases, the investor relies less on spoofing, and if the fine is large, the investor does not spoof the LOB. The arrival rate of buy MOs increases because other traders interpret the spoofed buy-heavy LOB as an upward pressure on prices. When the fine is low, spoofing considerably increases the revenues from liquidating a position. Spoofing increases the PnL because (i) the investor employs fewer MOs to draw the inventory to zero and benefits from roundtrip trades, which stem from spoof buy LOs that are ‘inadvertently’ filled and subsequently unwound with sell LOs; and (ii) the midprice trends upward when the book is buy-heavy; therefore the spoofer sells the asset at better prices. Journal: Applied Mathematical Finance Pages: 67-98 Issue: 1-2 Volume: 27 Year: 2020 Month: 7 X-DOI: 10.1080/1350486X.2020.1726783 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1726783 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:1-2:p:67-98 Template-Type: ReDIF-Article 1.0 Author-Name: Arvind Shrivats Author-X-Name-First: Arvind Author-X-Name-Last: Shrivats Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Optimal Generation and Trading in Solar Renewable Energy Certificate (SREC) Markets Abstract: SREC markets are a relatively novel market-based system to incentivize the production of energy from solar means. A regulator imposes a floor on the amount of energy each regulated firm must generate from solar power in a given period and provides them with certificates for each generated MWh. Firms offset these certificates against the floor and pay a penalty for any lacking certificates. Certificates are tradable assets, allowing firms to purchase/sell them freely. In this work, we formulate a stochastic control problem for generating and trading in SREC markets from a regulated firm’s perspective. We account for generation and trading costs, the impact both have on SREC prices, provide a characterization of the optimal strategy and develop a numerical algorithm to solve this control problem. Through numerical experiments, we explore how a firm who acts optimally behaves under various conditions. We find that an optimal firm’s generation and trading behaviour can be separated into various regimes, based on the marginal benefit of obtaining an additional SREC, and validate our theoretical characterization of the optimal strategy. We also conduct parameter sensitivity experiments. Journal: Applied Mathematical Finance Pages: 99-131 Issue: 1-2 Volume: 27 Year: 2020 Month: 7 X-DOI: 10.1080/1350486X.2020.1754260 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1754260 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:1-2:p:99-131 Template-Type: ReDIF-Article 1.0 Author-Name: Ben Hambly Author-X-Name-First: Ben Author-X-Name-Last: Hambly Author-Name: Jasdeep Kalsi Author-X-Name-First: Jasdeep Author-X-Name-Last: Kalsi Author-Name: James Newbury Author-X-Name-First: James Author-X-Name-Last: Newbury Title: Limit Order Books, Diffusion Approximations and Reflected SPDEs: From Microscopic to Macroscopic Models Abstract: Motivated by a zero-intelligence approach, the aim of this paper is to connect the microscopic (discrete price and volume), mesoscopic (discrete price and continuous volume) and macroscopic (continuous price and volume) frameworks for the modelling of limit order books, with a view to providing a natural probabilistic description of their behaviour in a high- to ultra high-frequency setting. Starting with a microscopic framework, we first examine the limiting behaviour of the order book process when order arrival and cancellation rates are sent to infinity and when volumes are considered to be of infinitesimal size. We then consider the transition between this mesoscopic model and a macroscopic model for the limit order book, obtained by letting the tick size tend to zero. The macroscopic limit can then be described using reflected SPDEs which typically arise in stochastic interface models. We then use financial data to discuss a possible calibration procedure for the model and illustrate numerically how it can reproduce observed behaviour of prices. This could then be used as a market simulator for short-term price prediction or for testing optimal execution strategies. Journal: Applied Mathematical Finance Pages: 132-170 Issue: 1-2 Volume: 27 Year: 2020 Month: 7 X-DOI: 10.1080/1350486X.2020.1758176 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1758176 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:1-2:p:132-170 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Divos Author-X-Name-First: Peter Author-X-Name-Last: Divos Author-Name: Sebastian Del Bano Rollin Author-X-Name-First: Sebastian Author-X-Name-Last: Del Bano Rollin Author-Name: Zsolt Bihari Author-X-Name-First: Zsolt Author-X-Name-Last: Bihari Author-Name: Tomaso Aste Author-X-Name-First: Tomaso Author-X-Name-Last: Aste Title: Risk-Neutral Pricing and Hedging of In-Play Football Bets Abstract: A risk-neutral valuation framework is developed for pricing and hedging in-play football bets based on modelling scores by independent Poisson processes with constant intensities. The Fundamental Theorems of Asset Pricing are applied to this set-up which enables us to derive novel arbitrage-free valuation formulæ for contracts currently traded in the market. We also describe how to calibrate the model to the market and how trades can be replicated and hedged. Journal: Applied Mathematical Finance Pages: 315-335 Issue: 4 Volume: 25 Year: 2018 Month: 7 X-DOI: 10.1080/1350486X.2018.1535275 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1535275 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:4:p:315-335 Template-Type: ReDIF-Article 1.0 Author-Name: Sidy Diop Author-X-Name-First: Sidy Author-X-Name-Last: Diop Author-Name: Andrea Pascucci Author-X-Name-First: Andrea Author-X-Name-Last: Pascucci Author-Name: Marco Di Francesco Author-X-Name-First: Marco Author-X-Name-Last: Di Francesco Author-Name: Gian Luca De Marchi Author-X-Name-First: Gian Luca Author-X-Name-Last: De Marchi Title: Sovereign CDS Calibration Under a Hybrid Sovereign Risk Model Abstract: The European sovereign debt crisis, started in the second half of 2011, has posed the problem for asset managers, trades and risk managers to assess sovereign default risk. In the reduced form framework, it is necessary to understand the interrelationship between creditworthiness of a sovereign, its intensity to default and the correlation with the exchange rate between the bond’s currency and the currency in which the Credit Default Swap CDS spread are quoted. To do this, we propose a hybrid sovereign risk model in which the intensity of default is based on the jump to default extended constant elasticity variance model. We analyse the differences between the default intensity under the domestic and foreign measure and we compute the default-survival probabilities in the bond’s currency measure. We also give an approximation formula to CDS spread obtained by perturbation theory and provide an efficient method to calibrate the model to CDS spread quoted by the market. Finally, we test the model on real market data by several calibration experiments to confirm the robustness of our method. Journal: Applied Mathematical Finance Pages: 336-360 Issue: 4 Volume: 25 Year: 2018 Month: 7 X-DOI: 10.1080/1350486X.2018.1554447 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1554447 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:4:p:336-360 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Pierre Fouque Author-X-Name-First: Jean-Pierre Author-X-Name-Last: Fouque Author-Name: Ruimeng Hu Author-X-Name-First: Ruimeng Author-X-Name-Last: Hu Title: Portfolio Optimization under Fast Mean-Reverting and Rough Fractional Stochastic Environment Abstract: Fractional stochastic volatility models have been widely used to capture the non-Markovian structure revealed from financial time series of realized volatility. On the other hand, empirical studies have identified scales in stock price volatility: both fast-timescale on the order of days and slow-scale on the order of months. So, it is natural to study the portfolio optimization problem under the effects of dependence behaviour which we will model by fractional Brownian motions with Hurst index $$H$$H , and in the fast or slow regimes characterized by small parameters $${\epsilon}$$ϵ or $$\delta $$δ . For the slowly varying volatility with $$H \in (0,1)$$H∈(0,1) , it was shown that the first order correction to the problem value contains two terms of the order $${\delta ^H}$$δH , one random component and one deterministic function of state processes, while for the fast varying case with $$H\, \gt\, {1 \over 2}$$H>12 , the same form holds an order $${{\epsilon}^{1 - H}}$$ϵ1−H . This paper is dedicated to the remaining case of a fast-varying rough environment ($$H \,\lt\, {1 \over 2}$$H<12 ) which exhibits a different behaviour. We show that, in the expansion, only one deterministic term of order $$\sqrt {\epsilon} $$ϵ appears in the first order correction. Journal: Applied Mathematical Finance Pages: 361-388 Issue: 4 Volume: 25 Year: 2018 Month: 7 X-DOI: 10.1080/1350486X.2019.1584532 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1584532 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:4:p:361-388 Template-Type: ReDIF-Article 1.0 Author-Name: José M. T. S. Cruz Author-X-Name-First: José M. T. S. Author-X-Name-Last: Cruz Author-Name: Daniel Ševčovič Author-X-Name-First: Daniel Author-X-Name-Last: Ševčovič Title: Option Pricing in Illiquid Markets with Jumps Abstract: The classical linear Black–Scholes model for pricing derivative securities is a popular model in the financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. The main purpose of this paper is to generalize the classical Black–Scholes model for pricing derivative securities by taking into account feedback effects due to an influence of a large trader on the underlying asset price dynamics exhibiting random jumps. The assumption that an investor can trade large amounts of assets without affecting the underlying asset price itself is usually not satisfied, especially in illiquid markets. We generalize the Frey–Stremme nonlinear option pricing model for the case the underlying asset follows a Lévy stochastic process with jumps. We derive and analyze a fully nonlinear parabolic partial-integro differential equation for the price of the option contract. We propose a semi-implicit numerical discretization scheme and perform various numerical experiments showing the influence of a large trader and intensity of jumps on the option price. Journal: Applied Mathematical Finance Pages: 389-409 Issue: 4 Volume: 25 Year: 2018 Month: 7 X-DOI: 10.1080/1350486X.2019.1585267 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1585267 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:4:p:389-409 Template-Type: ReDIF-Article 1.0 Author-Name: Chun-Yuan Chiu Author-X-Name-First: Chun-Yuan Author-X-Name-Last: Chiu Author-Name: Alec Kercheval Author-X-Name-First: Alec Author-X-Name-Last: Kercheval Title: Modelling Credit Risk in the Jump Threshold Framework Abstract: The jump threshold framework for credit risk modelling developed by Garreau and Kercheval enjoys the advantages of both structural- and reduced-form models. In their article, the focus is on multidimensional default dependence, under the assumptions that stock prices follow an exponential Lévy process (i.i.d. log returns) and that interest rates and stock volatility are constant. Explicit formulas for default time distributions and basket credit default swap (CDS) prices are obtained when the default threshold is deterministic, but only in terms of expectations when the default threshold is stochastic. In this article, we restrict attention to the one-dimensional, single-name case in order to obtain explicit closed-form solutions for the default time distribution when the default threshold, interest rate and volatility are all stochastic. When the interest rate and volatility processes are affine diffusions and the stochastic default threshold is properly chosen, we provide explicit formulas for the default time distribution, prices of defaultable bonds and CDS premia. The main idea is to make use of the Duffie–Pan–Singleton method of evaluating expectations of exponential integrals of affine diffusions. Journal: Applied Mathematical Finance Pages: 411-433 Issue: 5-6 Volume: 25 Year: 2018 Month: 11 X-DOI: 10.1080/1350486X.2018.1465349 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1465349 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:411-433 Template-Type: ReDIF-Article 1.0 Author-Name: Vadim Kaushansky Author-X-Name-First: Vadim Author-X-Name-Last: Kaushansky Author-Name: Alexander Lipton Author-X-Name-First: Alexander Author-X-Name-Last: Lipton Author-Name: Christoph Reisinger Author-X-Name-First: Christoph Author-X-Name-Last: Reisinger Title: Transition Probability of Brownian Motion in the Octant and its Application to Default Modelling Abstract: We derive a semi-analytical formula for the transition probability of three-dimensional Brownian motion in the positive octant with absorption at the boundaries. Separation of variables in spherical coordinates leads to an eigenvalue problem for the resulting boundary value problem in the two angular components. The main theoretical result is a solution to the original problem expressed as an expansion into special functions and an eigenvalue which has to be chosen to allow a matching of the boundary condition. We discuss and test several computational methods to solve a finite-dimensional approximation to this nonlinear eigenvalue problem. Finally, we apply our results to the computation of default probabilities and credit valuation adjustments in a structural credit model with mutual liabilities. Journal: Applied Mathematical Finance Pages: 434-465 Issue: 5-6 Volume: 25 Year: 2018 Month: 11 X-DOI: 10.1080/1350486X.2018.1481439 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1481439 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:434-465 Template-Type: ReDIF-Article 1.0 Author-Name: Sara Dutra Lopes Author-X-Name-First: Sara Dutra Author-X-Name-Last: Lopes Author-Name: Carlos Vázquez Author-X-Name-First: Carlos Author-X-Name-Last: Vázquez Title: Real-World Scenarios With Negative Interest Rates Based on the LIBOR Market Model Abstract: In this article, we present a methodology to simulate the evolution of interest rates under real-world probability measure. More precisely, using the multidimensional Shifted Lognormal LIBOR market model and a specification of the market price of risk vector process, we explain how to perform simulations of the real-world forward rates in the future, using the Euler‒Maruyama scheme with a predictor‒corrector strategy. The proposed methodology allows for the presence of negative interest rates as currently observed in the markets. Journal: Applied Mathematical Finance Pages: 466-482 Issue: 5-6 Volume: 25 Year: 2018 Month: 11 X-DOI: 10.1080/1350486X.2018.1492348 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1492348 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:466-482 Template-Type: ReDIF-Article 1.0 Author-Name: Hugo Eduardo Ramirez Author-X-Name-First: Hugo Eduardo Author-X-Name-Last: Ramirez Author-Name: Paul Johnson Author-X-Name-First: Paul Author-X-Name-Last: Johnson Author-Name: Peter Duck Author-X-Name-First: Peter Author-X-Name-Last: Duck Author-Name: Sydney Howell Author-X-Name-First: Sydney Author-X-Name-Last: Howell Title: The Optimal Interaction between a Hedge Fund Manager and Investor Abstract: This study explores hedge funds from the perspective of investors and the motivation behind their investments. We model a typical hedge fund contract between an investor and a manager, which includes the manager’s special reward scheme, i.e., partial ownership, incentives and early closure conditions. We present a continuous stochastic control problem for the manager’s wealth on a hedge fund comprising one risky asset and one riskless bond as a basis to calculate the investors’ wealth. Then we derive partial differential equations (PDEs) for each agent and numerically obtain the unique viscosity solution for these problems. Our model shows that the manager’s incentives are very high and therefore investors are not receiving profit compared to a riskless investment. We investigate a new type of hedge fund contract where the investor has the option to deposit additional money to the fund at half maturity time. Results show that investors’ inflow increases proportionally with the expected rate of return of the risky asset, but even in low rates of return, investors inflow money to keep the fund open. Finally, comparing the contracts with and without the option, we spot that investors are sometimes better off without the option to inflow money, thus creating a negative value of the option. Journal: Applied Mathematical Finance Pages: 483-510 Issue: 5-6 Volume: 25 Year: 2018 Month: 11 X-DOI: 10.1080/1350486X.2018.1506258 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1506258 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:483-510 Template-Type: ReDIF-Article 1.0 Author-Name: Julien Baptiste Author-X-Name-First: Julien Author-X-Name-Last: Baptiste Author-Name: Emmanuel Lépinette Author-X-Name-First: Emmanuel Author-X-Name-Last: Lépinette Title: Diffusion Equations: Convergence of the Functional Scheme Derived from the Binomial Tree with Local Volatility for Non Smooth Payoff Functions Abstract: The function solution to the functional scheme derived from the binomial tree financial model with local volatility converges to the solution of a diffusion equation of type $${h_t}(t,x) + {{{x^2}{\sigma ^2}(t,x)} \over 2}{h_{xx}}(t,x) = 0$$ht(t,x)+x2σ2(t,x)2hxx(t,x)=0 as the number of discrete dates $$n \to \infty $$n→∞ . Contrarily to classical numerical methods, in particular finite difference methods, the principle behind the functional scheme is only based on a discretization in time. We establish the uniform convergence in time of the scheme and provide the rate of convergence when the payoff function is not necessarily smooth as in finance. We illustrate the convergence result and compare its performance to the finite difference and finite element methods by numerical examples. Journal: Applied Mathematical Finance Pages: 511-532 Issue: 5-6 Volume: 25 Year: 2018 Month: 11 X-DOI: 10.1080/1350486X.2018.1513806 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1513806 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:511-532 Template-Type: ReDIF-Article 1.0 Author-Name: Ernst Eberlein Author-X-Name-First: Ernst Author-X-Name-Last: Eberlein Author-Name: Marcus Rudmann Author-X-Name-First: Marcus Author-X-Name-Last: Rudmann Title: Hybrid Lévy Models: Design and Computational Aspects Abstract: A hybrid model is a model, where two markets are studied jointly such that stochastic dependence can be taken into account. Such a dependence is well known for equity and interest rate markets on which we focus here. Other pairs can be considered in a similar way. Two different versions of a hybrid approach are developed. Independent time-inhomogeneous Lévy processes are used as the drivers of the dynamics of interest rates and equity. In both versions, the dynamics of the interest rate side is described by an equation for the instantaneous forward rate. Dependence between the markets is generated by introducing the driver of the interest rate market as an additional term into the dynamics of equity in the first version. The second version starts with the equity dynamics and uses a corresponding construction for the interest rate side. Dependence can be quantified in both cases by a single parameter. Numerically efficient valuation formulas for interest rate and equity derivatives are developed. Using market quotes for liquidly traded assets we show that the hybrid approach can be successfully calibrated. Journal: Applied Mathematical Finance Pages: 533-556 Issue: 5-6 Volume: 25 Year: 2018 Month: 11 X-DOI: 10.1080/1350486X.2018.1536523 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1536523 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:533-556 Template-Type: ReDIF-Article 1.0 Author-Name: Zsolt Nika Author-X-Name-First: Zsolt Author-X-Name-Last: Nika Author-Name: Miklos Rásonyi Author-X-Name-First: Miklos Author-X-Name-Last: Rásonyi Title: Log-Optimal Portfolios with Memory Effect Abstract: In portfolio optimization a classical problem is to trade with assets so as to maximize some kind of utility of the investor. In our paper this problem is investigated for assets whose prices depend on their past values in a non-Markovian way. Such models incorporate several features of real price processes better than Markov processes do. Our utility function is the widespread logarithmic utility, the formulation of the model is discrete in time. Despite the problem being a well-known one, there are few results where memory is treated systematically in a parametric model. Our algorithm is optimal and this optimality is guaranteed for a rich class of model specifications. Moreover, the algorithm runs online, i.e., the optimal investment is achieved in a day-by-day manner, using simple numerical integration, without Monte-Carlo simulations. Theoretical results are demonstrated by numerical experiments as well. Journal: Applied Mathematical Finance Pages: 557-585 Issue: 5-6 Volume: 25 Year: 2018 Month: 11 X-DOI: 10.1080/1350486X.2018.1542323 File-URL: http://hdl.handle.net/10.1080/1350486X.2018.1542323 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:5-6:p:557-585 Template-Type: ReDIF-Article 1.0 Author-Name: Dilip B. Madan Author-X-Name-First: Dilip B. Author-X-Name-Last: Madan Author-Name: King Wang Author-X-Name-First: King Author-X-Name-Last: Wang Title: Additive Processes with Bilateral Gamma Marginals Abstract: The Sato process associated with self decomposable laws at unit time is further generalized to an additive process with arbitrary innovation term structures. A second generalization to additive processes consistent with bilateral gamma marginal distributions is also made. The Sato process is a parametric special case of the two generalizations. This feature is exploited in defining calibration starting values. Calibration results are presented for $$1255$$1255 days of daily data on SPY options. The deterministic innovation variance model makes a median improvement of $$15\% $$15% in root-mean-square error over the Sato process. The comparable value for the general additive process is $$40\%.$$40%. The Sato process relative to the general additive process overprices negative moves and underprices positive ones. The underpricing of negative moves decreases with maturity. On the positive side, the overpricing decreases with maturity. For negative moves, the overpricing is larger for smaller moves, while for positive moves the underpricing is larger for the larger moves. Journal: Applied Mathematical Finance Pages: 171-188 Issue: 3 Volume: 27 Year: 2020 Month: 05 X-DOI: 10.1080/1350486X.2020.1779597 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1779597 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:3:p:171-188 Template-Type: ReDIF-Article 1.0 Author-Name: Simon Schnürch Author-X-Name-First: Simon Author-X-Name-Last: Schnürch Author-Name: Andreas Wagner Author-X-Name-First: Andreas Author-X-Name-Last: Wagner Title: Electricity Price Forecasting with Neural Networks on EPEX Order Books Abstract: This paper employs machine learning algorithms to forecast German electricity spot market prices. The forecasts utilize in particular bid and ask order book data from the spot market but also fundamental market data like renewable infeed and expected total demand. Appropriate feature extraction for the order book data is developed proceeding from existing literature. Using cross-validation to optimize hyperparameters, neural networks and random forests are fit to the data. Their in-sample and out-of-sample performance is compared to statistical reference models. The machine learning models outperform traditional approaches. Journal: Applied Mathematical Finance Pages: 189-206 Issue: 3 Volume: 27 Year: 2020 Month: 05 X-DOI: 10.1080/1350486X.2020.1805337 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1805337 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:3:p:189-206 Template-Type: ReDIF-Article 1.0 Author-Name: Piergiacomo Sabino Author-X-Name-First: Piergiacomo Author-X-Name-Last: Sabino Title: Exact Simulation of Variance Gamma-Related OU Processes: Application to the Pricing of Energy Derivatives Abstract: In this study we use a three-step procedure that relates the self-decomposability of the stationary law of a generalized Ornstein-Uhlenbeck process to the transition law of such processes. Based on this procedure and the results of Qu, Dassios, and Zhao (2019), we derive the exact simulation, without numerical inversion, of the skeleton of a Variance Gamma and of a symmetric Variance Gamma driven Ornstein-Uhlenbeck process. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms. These results are instrumental to simulate the spot price dynamics in energy markets and to price Asian options and gas storages by Monte Carlo simulations in a framework similar to the one discussed in Cummins, Kiely and Murphy (2017, 2018). Journal: Applied Mathematical Finance Pages: 207-227 Issue: 3 Volume: 27 Year: 2020 Month: 05 X-DOI: 10.1080/1350486X.2020.1813040 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1813040 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:3:p:207-227 Template-Type: ReDIF-Article 1.0 Author-Name: Shi Qiu Author-X-Name-First: Shi Author-X-Name-Last: Qiu Title: American Strangle Options Abstract: In this paper, we show that the double optimal stopping boundaries for American strangle options with finite horizon can be characterized as the unique pair of solution to a system of two nonlinear integral equations arising from the early exercise premium (EEP) representation. The proof of EEP representation is based on the change-of-variable formula with local time on curves. After comparing the return of the alternative portfolio including an American call and an American put option, we find that it is more preferable for an investor to select American strangle options to hedge an underlying asset with high volatility. Journal: Applied Mathematical Finance Pages: 228-263 Issue: 3 Volume: 27 Year: 2020 Month: 05 X-DOI: 10.1080/1350486X.2020.1825968 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1825968 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:3:p:228-263 Template-Type: ReDIF-Article 1.0 Author-Name: José M. T. S. Cruz Author-X-Name-First: José M. T. S. Author-X-Name-Last: Cruz Author-Name: Daniel Ševčovič Author-X-Name-First: Daniel Author-X-Name-Last: Ševčovič Title: Option Pricing in Illiquid Markets with Jumps Abstract: The classical linear Black–Scholes model for pricing derivative securities is a popular model in the financial industry. It relies on several restrictive assumptions such as completeness, and frictionless of the market as well as the assumption on the underlying asset price dynamics following a geometric Brownian motion. The main purpose of this paper is to generalize the classical Black–Scholes model for pricing derivative securities by taking into account feedback effects due to an influence of a large trader on the underlying asset price dynamics exhibiting random jumps. The assumption that an investor can trade large amounts of assets without affecting the underlying asset price itself is usually not satisfied, especially in illiquid markets. We generalize the Frey–Stremme nonlinear option pricing model for the case the underlying asset follows a Lévy stochastic process with jumps. We derive and analyze a fully nonlinear parabolic partial-integro differential equation for the price of the option contract. We propose a semi-implicit numerical discretization scheme and perform various numerical experiments showing the influence of a large trader and intensity of jumps on the option price. Journal: Applied Mathematical Finance Pages: 395-415 Issue: 4 Volume: 25 Year: 2018 Month: 7 X-DOI: 10.1080/1350486X.2019.1585267 File-URL: http://hdl.handle.net/10.1080/1350486X.2019.1585267 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:25:y:2018:i:4:p:395-415 Template-Type: ReDIF-Article 1.0 Author-Name: George Bouzianis Author-X-Name-First: George Author-X-Name-Last: Bouzianis Author-Name: Lane P. Hughston Author-X-Name-First: Lane P. Author-X-Name-Last: Hughston Title: Optimal Hedging in Incomplete Markets Abstract: We consider the problem of optimal hedging in an incomplete market with an established pricing kernel. In such a market, prices are uniquely determined, but perfect hedges are usually not available. We work in the rather general setting of a Lévy-Ito market, where assets are driven jointly by an n-dimensional Brownian motion and an independent Poisson random measure on an n-dimensional state space. Given a position in need of hedging and the instruments available as hedges, we demonstrate the existence of an optimal hedge portfolio, where optimality is defined by use of a least expected squared error criterion over a specified time frame, and where the numeraire with respect to which the hedge is optimized is taken to be the benchmark process associated with the designated pricing kernel. Journal: Applied Mathematical Finance Pages: 265-287 Issue: 4 Volume: 27 Year: 2020 Month: 07 X-DOI: 10.1080/1350486X.2020.1819831 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1819831 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:4:p:265-287 Template-Type: ReDIF-Article 1.0 Author-Name: M.E. Mancino Author-X-Name-First: M.E. Author-X-Name-Last: Mancino Author-Name: S. Scotti Author-X-Name-First: S. Author-X-Name-Last: Scotti Author-Name: G. Toscano Author-X-Name-First: G. Author-X-Name-Last: Toscano Title: Is the Variance Swap Rate Affine in the Spot Variance? Evidence from S&P500 Data Abstract: We empirically investigate the functional link between the variance swap rate and the spot variance. Using S&P500 data over the period 2006–2018, we find overwhelming empirical evidence supporting the affine link implied by exponential affine stochastic volatility models. Tests on yearly subsamples suggest that exponential mean-reverting variance models provide a good fit during periods of extreme volatility, while polynomial modelsare suited for years characterized by more frequent price jumps. Journal: Applied Mathematical Finance Pages: 288-316 Issue: 4 Volume: 27 Year: 2020 Month: 07 X-DOI: 10.1080/1350486X.2020.1847671 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1847671 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:4:p:288-316 Template-Type: ReDIF-Article 1.0 Author-Name: Ryan Donnelly Author-X-Name-First: Ryan Author-X-Name-Last: Donnelly Author-Name: Matthew Lorig Author-X-Name-First: Matthew Author-X-Name-Last: Lorig Title: Optimal Trading with Differing Trade Signals Abstract: We consider the problem of maximizing portfolio value when an agent has a subjective view on asset value which differs from the traded market price. The agent’s trades will have a price impact which affects the price at which the asset is traded. In addition to the agent’s trades affecting the market price, the agent may change his view on the asset’s value if its difference from the market price persists. We also consider a situation of several agents interacting and trading simultaneously when they have a subjective view of the asset value. Two cases of the subjective views of agents are considered: one in which they all share the same information, and one in which they all have an individual signal correlated with price innovations. To study the large agent problem we take a mean-field game approach which remains tractable. After classifying the mean-field equilibrium we compute the cross-sectional distribution of agents’ inventories and the dependence of price distribution on the amount of shared information among the agents. Journal: Applied Mathematical Finance Pages: 317-344 Issue: 4 Volume: 27 Year: 2020 Month: 07 X-DOI: 10.1080/1350486X.2020.1847672 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1847672 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:4:p:317-344 Template-Type: ReDIF-Article 1.0 Author-Name: Samuel N. Cohen Author-X-Name-First: Samuel N. Author-X-Name-Last: Cohen Author-Name: Christoph Reisinger Author-X-Name-First: Christoph Author-X-Name-Last: Reisinger Author-Name: Sheng Wang Author-X-Name-First: Sheng Author-X-Name-Last: Wang Title: Detecting and Repairing Arbitrage in Traded Option Prices Abstract: Option price data are used as inputs for model calibration, risk-neutral density estimation and many other financial applications. The presence of arbitrage in option price data can lead to poor performance or even failure of these tasks, making pre-processing of the data to eliminate arbitrage necessary. Most attention in the relevant literature has been devoted to arbitrage-free smoothing and filtering (i.e., removing) of data. In contrast to smoothing, which typically changes nearly all data, or filtering, which truncates data, we propose to repair data by only necessary and minimal changes. We formulate the data repair as a linear programming (LP) problem, where the no-arbitrage relations are constraints, and the objective is to minimize prices’ changes within their bid and ask price bounds. Through empirical studies, we show that the proposed arbitrage repair method gives sparse perturbations on data, and is fast when applied to real-world large-scale problems due to the LP formulation. In addition, we show that removing arbitrage from prices data by our repair method can improve model calibration with enhanced robustness and reduced calibration error. Journal: Applied Mathematical Finance Pages: 345-373 Issue: 5 Volume: 27 Year: 2020 Month: 09 X-DOI: 10.1080/1350486X.2020.1846573 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1846573 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:5:p:345-373 Template-Type: ReDIF-Article 1.0 Author-Name: Michael Roberts Author-X-Name-First: Michael Author-X-Name-Last: Roberts Author-Name: Indranil SenGupta Author-X-Name-First: Indranil Author-X-Name-Last: SenGupta Title: Sequential Hypothesis Testing in Machine Learning, and Crude Oil Price Jump Size Detection Abstract: In this paper, we present a sequential hypothesis test for the detection of the distribution of jump size in Lévy processes. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analysed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the data set, and the deterministic component is implemented to improve the Barndorff-Nielsen & Shephard model, a commonly used stochastic model for derivative and commodity market analysis. Journal: Applied Mathematical Finance Pages: 374-395 Issue: 5 Volume: 27 Year: 2020 Month: 09 X-DOI: 10.1080/1350486X.2020.1859943 File-URL: http://hdl.handle.net/10.1080/1350486X.2020.1859943 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:5:p:374-395 Template-Type: ReDIF-Article 1.0 Author-Name: Ernst Eberlein Author-X-Name-First: Ernst Author-X-Name-Last: Eberlein Author-Name: Christoph Gerhart Author-X-Name-First: Christoph Author-X-Name-Last: Gerhart Author-Name: Eva Lütkebohmert Author-X-Name-First: Eva Author-X-Name-Last: Lütkebohmert Title: A Multiple Curve Lévy Swap Market Model Abstract: In this paper, we develop an arbitrage-free multiple curve model through the specification of forward swap rates. Two sets of assets are chosen as fundamentals: OIS zero-coupon bonds and forward rate agreements. This is a very natural approach since, on the one hand, OIS bonds represent the class of risk-free discount bonds and, on the other hand, the mid and long maturity part of the interest rate term structure is bootstrapped from quotes of swap rates that can be represented by FRA rates and OIS bond prices in the multiple curve setting. We construct the rates via a backward induction along the tenor structure on the basis of the forward swap measures. Time-inhomogeneous Lévy processes are used as drivers of the dynamics. As an application, we derive an approximative Fourier-based valuation formula for swaptions. The model is implemented and calibrated by using generalized hyperbolic Lévy processes as drivers. Journal: Applied Mathematical Finance Pages: 396-421 Issue: 5 Volume: 27 Year: 2020 Month: 09 X-DOI: 10.1080/1350486X.2021.1877559 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1877559 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:5:p:396-421 Template-Type: ReDIF-Article 1.0 Author-Name: Chanaka Edirisinghe Author-X-Name-First: Chanaka Author-X-Name-Last: Edirisinghe Author-Name: Yonggan Zhao Author-X-Name-First: Yonggan Author-X-Name-Last: Zhao Title: Smart Indexing Under Regime-Switching Economic States Abstract: Index funds that track a benchmark, such as the market cap-weighted S&P 500 index, tend to have portfolio holdings biased towards slower-growth large-cap equities that result in the fund’s under-performance, especially in economic downturns. We develop a rigorous quantitative framework that allows dynamic-rebalancing of the allocations such that portfolio exposure in a market segment can change periodically based on economic activity, measured via a set of macro-economic and financial indicators. The method incorporates potential shifts in the economic state, and the likelihood thereof, to determine the fund’s risk orientation optimally in tracking or not tracking the benchmark index. That is, the greater the likelihood of a stronger economic state, the higher the degree of tracking the market index; however, a lack of confidence in the economic state results in a more index-neutral portfolio composition. The proposed smart indexing optimal strategy generates superior risk-adjusted returns consistently in out-of-sample testing, relative to (pure) index tracking. We test several variants and present sensitivity analyses that support our actively-managed smart indexing approach. Journal: Applied Mathematical Finance Pages: 422-456 Issue: 5 Volume: 27 Year: 2020 Month: 09 X-DOI: 10.1080/1350486X.2021.1891554 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1891554 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:5:p:422-456 Template-Type: ReDIF-Article 1.0 Author-Name: Peter Carr Author-X-Name-First: Peter Author-X-Name-Last: Carr Author-Name: Gianna Figà-Talamanca Author-X-Name-First: Gianna Author-X-Name-Last: Figà-Talamanca Title: Spiking the Volatility Punch Abstract: An alternative volatility index called SPIKES has been recently introduced. Like VIX, SPIKES aims to forecast S&P 500 volatility over a 30-day horizon and both indexes are based on the same theoretical formula; yet, they differ in several ways. While some differences are introduced in response to the controversy surrounding possible VIX manipulation, others are due to the choice of the S&P500 exchange-traded fund (ETF), named SPY, as a substitute for the S&P500 (SPX) Index itself. Indeed, options on the SPX, used for VIX computation, are European-style, whereas options on the SPY ETF, used for SPIKES computation, are American-style.Overall, the difference is mainly due to the early exercise premium of the component options and the dividend timing of the underlying SPY versus SPX and we assess the magnitude of these separate contributions under the benchmark Black, Merton and Scholes setting. By applying both the finite difference method and newly-derived approximation formulas we show that the new SPIKES index will track the VIX index as long as 30-day US interest rates and annualized dividend yields continue to be range-bound between 0 and 10% per year. Hence, after more that 20 years of supremacy, VIX may have found its first competitor. Journal: Applied Mathematical Finance Pages: 495-520 Issue: 6 Volume: 27 Year: 2020 Month: 11 X-DOI: 10.1080/1350486X.2021.1893196 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1893196 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:6:p:495-520 Template-Type: ReDIF-Article 1.0 Author-Name: Richard Biegler-König Author-X-Name-First: Richard Author-X-Name-Last: Biegler-König Title: Hedging Strategies in Commodity Markets – Rolling Intrinsic and Delta Hedging for Virtual Power Plants Abstract: Hedging on commodity markets is usually done by applying either the rolling intrinsic strategy or the canonical delta hedge strategy. In this paper we introduce, compare and discuss both hedging strategies in the context of virtual power plants (VPP). We formulate the precise relationship of the two strategies mathematically. Our main result is that they are not only very similar regarding hedge construction but also that both strategies are equal in expectation. The proof involves some stochastic calculus and the Brownian local time. We illustrate our findings with simulated data as well as in prototypical market scenarios. These studies show that the rolling intrinsic hedge comes with a riskier profile than the delta hedge. Journal: Applied Mathematical Finance Pages: 550-582 Issue: 6 Volume: 27 Year: 2020 Month: 11 X-DOI: 10.1080/1350486X.2021.1898998 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1898998 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:6:p:550-582 Template-Type: ReDIF-Article 1.0 Author-Name: Terry Lyons Author-X-Name-First: Terry Author-X-Name-Last: Lyons Author-Name: Sina Nejad Author-X-Name-First: Sina Author-X-Name-Last: Nejad Author-Name: Imanol Perez Arribas Author-X-Name-First: Imanol Author-X-Name-Last: Perez Arribas Title: Non-parametric Pricing and Hedging of Exotic Derivatives Abstract: In the spirit of Arrow–Debreu, we introduce a family of financial derivatives that act as primitive securities in that exotic derivatives can be approximated by their linear combinations. We call these financial derivatives signature payoffs. We show that signature payoffs can be used to non-parametrically price and hedge exotic derivatives in the scenario where one has access to price data for other exotic payoffs. The methodology leads to a computationally tractable and accurate algorithm for pricing and hedging using market prices of a basket of exotic derivatives that has been tested on real and simulated market prices, obtaining good results. Journal: Applied Mathematical Finance Pages: 457-494 Issue: 6 Volume: 27 Year: 2020 Month: 11 X-DOI: 10.1080/1350486X.2021.1891555 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1891555 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:6:p:457-494 Template-Type: ReDIF-Article 1.0 Author-Name: Martin D. Gould Author-X-Name-First: Martin D. Author-X-Name-Last: Gould Author-Name: Nikolaus Hautsch Author-X-Name-First: Nikolaus Author-X-Name-Last: Hautsch Author-Name: Sam D. Howison Author-X-Name-First: Sam D. Author-X-Name-Last: Howison Author-Name: Mason A. Porter Author-X-Name-First: Mason A. Author-X-Name-Last: Porter Title: Counterparty Credit Limits: The Impact of a Risk-Mitigation Measure on Everyday Trading Abstract: A counterparty credit limit (CCL) is a limit that is imposed by a financial institution to cap its maximum possible exposure to a specified counterparty. CCLs help institutions to mitigate counterparty credit risk via selective diversification of their exposures. In this paper, we analyse how CCLs impact the prices that institutions pay for their trades during everyday trading. We study a high-quality data set from a large electronic trading platform in the foreign exchange spot market that allows institutions to apply CCLs. We find empirically that CCLs had little impact on the vast majority of trades in this data set. We also study the impact of CCLs using a new model of trading. By simulating our model with different underlying CCL networks, we highlight that CCLs can have a major impact in some situations. Journal: Applied Mathematical Finance Pages: 520-548 Issue: 6 Volume: 27 Year: 2020 Month: 11 X-DOI: 10.1080/1350486X.2021.1893770 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1893770 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:27:y:2020:i:6:p:520-548 Template-Type: ReDIF-Article 1.0 Author-Name: The Editors Title: Correction Journal: Applied Mathematical Finance Pages: 96-99 Issue: 1 Volume: 28 Year: 2021 Month: 01 X-DOI: 10.1080/1350486X.2021.1956708 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1956708 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:1:p:96-99 Template-Type: ReDIF-Article 1.0 Author-Name: Jean-Philippe Aguilar Author-X-Name-First: Jean-Philippe Author-X-Name-Last: Aguilar Author-Name: Nicolas Pesci Author-X-Name-First: Nicolas Author-X-Name-Last: Pesci Author-Name: Victor James Author-X-Name-First: Victor Author-X-Name-Last: James Title: A Structural Approach to Default Modelling with Pure Jump Processes Abstract: We present a general framework for the estimation of corporate default based on a firm’s capital structure, when its assets are assumed to follow a pure jump Lévy processes; this setup provides a natural extension to usual default metrics defined in diffusion (log-normal) models, and allows to capture extreme market events such as sudden drops in asset prices, which are closely linked to default occurrence. Within this framework, we introduce several pure jump processes featuring negative jumps only and derive practical closed formulas for equity prices, which enable us to use a moment-based algorithm to calibrate the parameters from real market data and to estimate the associated default metrics. A notable feature of these models is the redistribution of credit risk towards shorter maturity: this constitutes an interesting improvement to diffusion models, which are known to underestimate short-term default probabilities. We also provide extensions to a model featuring both positive and negative jumps and discuss qualitative and quantitative features of the results. For readers convenience, practical tools for model implementation and GitHub links are also included. Journal: Applied Mathematical Finance Pages: 48-78 Issue: 1 Volume: 28 Year: 2021 Month: 01 X-DOI: 10.1080/1350486X.2021.1957956 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1957956 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:1:p:48-78 Template-Type: ReDIF-Article 1.0 Author-Name: Zihao Zhang Author-X-Name-First: Zihao Author-X-Name-Last: Zhang Author-Name: Bryan Lim Author-X-Name-First: Bryan Author-X-Name-Last: Lim Author-Name: Stefan Zohren Author-X-Name-First: Stefan Author-X-Name-Last: Zohren Title: Deep Learning for Market by Order Data Abstract: Market by order (MBO) data – a detailed feed of individual trade instructions for a given stock on an exchange – is arguably one of the most granular sources of microstructure information. While limit order books (LOBs) are implicitly derived from it, MBO data is largely neglected by current academic literature, which focuses primarily on LOB modelling. In this paper, we demonstrate the utility of MBO data for forecasting high-frequency price movements, providing an orthogonal source of information to LOB snapshots and expanding the universe of alpha discovery. We provide the first predictive analysis on MBO data by carefully introducing the data structure and presenting a specific normalization scheme to consider level information in order books and to allow model training with multiple instruments. Through forecasting experiments using deep neural networks, we show that while MBO-driven and LOB-driven models individually provide similar performance, ensembles of the two can lead to improvements in forecasting accuracy – indicating that MBO data is additive to LOB-based features. Journal: Applied Mathematical Finance Pages: 79-95 Issue: 1 Volume: 28 Year: 2021 Month: 01 X-DOI: 10.1080/1350486X.2021.1967767 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1967767 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:1:p:79-95 Template-Type: ReDIF-Article 1.0 Author-Name: Piergiacomo Sabino Author-X-Name-First: Piergiacomo Author-X-Name-Last: Sabino Author-Name: Nicola Cufaro Petroni Author-X-Name-First: Nicola Author-X-Name-Last: Cufaro Petroni Title: Fast Pricing of Energy Derivatives with Mean-Reverting Jump-diffusion Processes Abstract: Most energy and commodity markets exhibit mean-reversion and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. To this end, in this paper we present a few fast and efficient methodologies for the exact simulation of the spot price dynamics modelled as the exponential of the sum of a Gaussian Ornstein-Uhlenbeck process and an independent pure jump process, where the latter one is driven by a compound Poisson process with (bilateral) exponentially distributed jumps. These methodologies are finally applied to the pricing of Asian options, gas and hydro storages and swing options under different combinations of jump-diffusion market models, and the apparent computational advantages of the proposed procedures are emphasized. Journal: Applied Mathematical Finance Pages: 1-22 Issue: 1 Volume: 28 Year: 2021 Month: 01 X-DOI: 10.1080/1350486X.2021.1909488 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1909488 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:1:p:1-22 Template-Type: ReDIF-Article 1.0 Author-Name: Markus Hess Author-X-Name-First: Markus Author-X-Name-Last: Hess Title: Explicit Representations for Utility Indifference Prices Abstract: In this paper, we apply stochastic maximum principles to derive representations for exponential utility indifference prices. We also obtain the related optimal portfolio processes and utility indifference hedging strategies. To illustrate our theoretical results, we present several concrete examples and study the limit behaviour of utility indifference prices for vanishing and infinite risk aversion. We further investigate how the optimal trading strategies and utility indifference prices alter if one assumes that an investor has some additional information on the future behaviour of the underlying stock price process available. In this regard, we propose a customized enlarged filtration approach and deduce a formula for the utility indifference price in this extended setup. We finally provide a representation for the information premium in our utility indifference pricing framework. Journal: Applied Mathematical Finance Pages: 23-47 Issue: 1 Volume: 28 Year: 2021 Month: 01 X-DOI: 10.1080/1350486X.2021.1922297 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1922297 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:1:p:23-47 Template-Type: ReDIF-Article 1.0 Author-Name: Philippe Bergault Author-X-Name-First: Philippe Author-X-Name-Last: Bergault Author-Name: David Evangelista Author-X-Name-First: David Author-X-Name-Last: Evangelista Author-Name: Olivier Guéant Author-X-Name-First: Olivier Author-X-Name-Last: Guéant Author-Name: Douglas Vieira Author-X-Name-First: Douglas Author-X-Name-Last: Vieira Title: Closed-form Approximations in Multi-asset Market Making Abstract: A large proportion of market making models derive from the seminal model of Avellaneda and Stoikov. The numerical approximation of the value function and the optimal quotes in these models remains a challenge when the number of assets is large. In this article, we propose closed-form approximations for the value functions of many multi-asset extensions of the Avellaneda–Stoikov model. These approximations or proxies can be used (i) as heuristic evaluation functions, (ii) as initial value functions in reinforcement learning algorithms, and/or (iii) directly to design quoting strategies through a greedy approach. Regarding the latter, our results lead to new and easily interpretable closed-form approximations for the optimal quotes, both in the finite-horizon case and in the asymptotic (ergodic) regime. Journal: Applied Mathematical Finance Pages: 101-142 Issue: 2 Volume: 28 Year: 2021 Month: 03 X-DOI: 10.1080/1350486X.2021.1949359 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1949359 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:2:p:101-142 Template-Type: ReDIF-Article 1.0 Author-Name: Matteo Gardini Author-X-Name-First: Matteo Author-X-Name-Last: Gardini Author-Name: Piergiacomo Sabino Author-X-Name-First: Piergiacomo Author-X-Name-Last: Sabino Author-Name: Emanuela Sasso Author-X-Name-First: Emanuela Author-X-Name-Last: Sasso Title: A Bivariate Normal Inverse Gaussian Process with Stochastic Delay: Efficient Simulations and Applications to Energy Markets Abstract: Using the concept of self-decomposable subordinators introduced by Gardini, Sabino, and Sasso, we build a new bivariate Normal Inverse Gaussian process that can capture stochastic delays. In addition, we also develop a novel path simulation scheme that relies on the mathematical connection between self-decomposable Inverse Gaussian laws and Lévy-driven Ornstein–Uhlenbeck processes with Inverse Gaussian stationary distribution. We show that our approach provides an improvement to the existing simulation scheme detailed in Zhang and Zhang, because it does not rely on an acceptance–rejection method. Eventually, these results are applied to the modelling of energy markets and to the pricing of spread options using the proposed Monte Carlo scheme and Fourier techniques. Journal: Applied Mathematical Finance Pages: 178-199 Issue: 2 Volume: 28 Year: 2021 Month: 03 X-DOI: 10.1080/1350486X.2021.2010106 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.2010106 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:2:p:178-199 Template-Type: ReDIF-Article 1.0 Author-Name: Jose S. Penalva Author-X-Name-First: Jose S. Author-X-Name-Last: Penalva Author-Name: Mikel Tapia Author-X-Name-First: Mikel Author-X-Name-Last: Tapia Title: Heterogeneity and Competition in Fragmented Markets: Fees Vs Speed Abstract: This paper provides an integrated overview of the effects of the implementation of the SEC’s Tick Pilot program on liquidity and competition in U.S. markets, separated into three groups by tick size. We confirm the standard effects of tick size changes on quoted spreads, realized spreads, and depth, as well as the role of the size of the quoted spread prior to the change in tick size. We add that the increase in the tick size leads to a significant reduction in the frequency and magnitude of price changes, primarily driven by a reduction in the frequency of aggressive limit orders. The major effect of the tick size is to alter competition by driving trading volume to inverted fee and off-exchange venues. We find that traders prefer a larger price improvement rather than lower latency for the smallest tick stocks while the reverse is true for largest tick stocks. Overall, the effect of the tick change has an insignificant effect on volume except for stocks with the smallest tick sizes subject to the trade-at rule, who see a substantial drop in volume. Journal: Applied Mathematical Finance Pages: 143-177 Issue: 2 Volume: 28 Year: 2021 Month: 03 X-DOI: 10.1080/1350486X.2021.1960574 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.1960574 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:2:p:143-177 Template-Type: ReDIF-Article 1.0 Author-Name: Dilip B. Madan Author-X-Name-First: Dilip B. Author-X-Name-Last: Madan Author-Name: King Wang Author-X-Name-First: King Author-X-Name-Last: Wang Title: Risk Neutral Jump Arrival Rates Implied in Option Prices and Their Models Abstract: Characteristic functions of risk neutral densities are constructed from the prices of options at a fixed maturity using well-known procedures. The logarithm of these characteristic functions are shown to synthesize the Fourier transform of jump arrival tails. The formal arrival rate tails are actual arrival rates if their derivatives have an appropriate sign. The derivatives of formal arrival rate tails embedded in option prices are observed on occasion to be negative, reflecting signed jump arrival rates. Although puzzling at first, we further observe that simple analytical cosine perturbations of the symmetric variance gamma Lévy density provides theoretical examples of such signed arrival rates consistent with a probability density. Additionally signed arrival rates also arise when models of signals perturbed by independent noise yield examples of characteristic functions for signal densities that are ratios of pure jump infinitely divisible characteristic functions. Such ratio characteristic functions can reflect signed arrival rates. Specific models using ratios of bilateral gamma and CGMY models are developed and calibrated to short maturity option prices. The ratio models provide significant improvements over their non-ratio counterparts. The models fall in the class of what have recently been termed to be quasi-infinitely divisible distributions. Journal: Applied Mathematical Finance Pages: 201-235 Issue: 3 Volume: 28 Year: 2021 Month: 05 X-DOI: 10.1080/1350486X.2021.2007145 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.2007145 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:3:p:201-235 Template-Type: ReDIF-Article 1.0 Author-Name: Marco Avellaneda Author-X-Name-First: Marco Author-X-Name-Last: Avellaneda Author-Name: Thomas Nanfeng Li Author-X-Name-First: Thomas Nanfeng Author-X-Name-Last: Li Author-Name: Andrew Papanicolaou Author-X-Name-First: Andrew Author-X-Name-Last: Papanicolaou Author-Name: Gaozhan Wang Author-X-Name-First: Gaozhan Author-X-Name-Last: Wang Title: Trading Signals in VIX Futures Abstract: We propose a new approach for trading VIX futures. We assume that the term structure of VIX futures follows a Markov model. Our trading strategy selects a position in VIX futures by maximizing the expected utility for a day-ahead horizon given the current shape and level of the term structure. Computationally, we model the functional dependence between the VIX futures curve, the VIX futures positions, and the expected utility as a deep neural network with five hidden layers. Out-of-sample backtests of the VIX futures trading strategy suggest that this approach gives rise to reasonable portfolio performance, and to positions in which the investor will be either long or short VIX futures contracts depending on the market environment. Journal: Applied Mathematical Finance Pages: 275-298 Issue: 3 Volume: 28 Year: 2021 Month: 05 X-DOI: 10.1080/1350486X.2021.2010584 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.2010584 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:3:p:275-298 Template-Type: ReDIF-Article 1.0 Author-Name: Arjun Prakash Author-X-Name-First: Arjun Author-X-Name-Last: Prakash Author-Name: Nick James Author-X-Name-First: Nick Author-X-Name-Last: James Author-Name: Max Menzies Author-X-Name-First: Max Author-X-Name-Last: Menzies Author-Name: Gilad Francis Author-X-Name-First: Gilad Author-X-Name-Last: Francis Title: Structural Clustering of Volatility Regimes for Dynamic Trading Strategies Abstract: We develop a new method to find the number of volatility regimes in a nonstationary financial time series by applying unsupervised learning to its volatility structure. We use change point detection to partition a time series into locally stationary segments and then compute a distance matrix between segment distributions. The segments are clustered into a learned number of discrete volatility regimes via an optimization routine. Using this framework, we determine the volatility clustering structure for financial indices, large-cap equities, exchange-traded funds and currency pairs. Our method overcomes the rigid assumptions necessary to implement many parametric regime-switching models while effectively distilling a time series into several characteristic behaviours. Our results provide a significant simplification of these time series and a strong descriptive analysis of prior behaviours of volatility. Finally, we create and validate a dynamic trading strategy that learns the optimal match between the current distribution of a time series and its past regimes, thereby making online risk-avoidance decisions at present. Journal: Applied Mathematical Finance Pages: 236-274 Issue: 3 Volume: 28 Year: 2021 Month: 05 X-DOI: 10.1080/1350486X.2021.2007146 File-URL: http://hdl.handle.net/10.1080/1350486X.2021.2007146 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:3:p:236-274 Template-Type: ReDIF-Article 1.0 Author-Name: Brian Ning Author-X-Name-First: Brian Author-X-Name-Last: Ning Author-Name: Franco Ho Ting Lin Author-X-Name-First: Franco Ho Ting Author-X-Name-Last: Lin Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Double Deep Q-Learning for Optimal Execution Abstract: Optimal trade execution is an important problem faced by essentially all traders. Much research into optimal execution uses stringent model assumptions and applies continuous time stochastic control to solve them. Here, we instead take a model free approach and develop a variation of Deep Q-Learning to estimate the optimal actions of a trader. The model is a fully connected Neural Network trained using Experience Replay and Double DQN with input features given by the current state of the limit order book, other trading signals, and available execution actions, while the output is the Q-value function estimating the future rewards under an arbitrary action. We apply our model to nine different stocks and find that it outperforms the standard benchmark approach on most stocks using the measures of (i) mean and median out-performance, (ii) probability of out-performance, and (iii) gain-loss ratios. Journal: Applied Mathematical Finance Pages: 361-380 Issue: 4 Volume: 28 Year: 2021 Month: 07 X-DOI: 10.1080/1350486X.2022.2077783 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2077783 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:4:p:361-380 Template-Type: ReDIF-Article 1.0 Author-Name: Mike Ludkovski Author-X-Name-First: Mike Author-X-Name-Last: Ludkovski Author-Name: Yuri Saporito Author-X-Name-First: Yuri Author-X-Name-Last: Saporito Title: KrigHedge: Gaussian Process Surrogates for Delta Hedging Abstract: We investigate a machine learning approach to option Greeks approximation based on Gaussian Process (GP) surrogates. Our motivation is to implement Delta hedging in cases where direct computation is expensive, such as in local volatility models, or can only ever be done approximately. The proposed method takes in noisily observed option prices, fits a non-parametric input-output map and then analytically differentiates the latter to obtain the various price sensitivities. Thus, a single surrogate yields multiple self-consistent Greeks. We provide a detailed analysis of numerous aspects of GP surrogates, including choice of kernel family, simulation design, choice of trend function and impact of noise. We moreover connect the quality of the Delta approximation to the resulting discrete-time hedging loss. Results are illustrated with two extensive case studies that consider estimation of Delta, Theta and Gamma and benchmark approximation quality and uncertainty quantification using a variety of statistical metrics. Among our key take-aways are the recommendation to use Matérn kernels, the benefit of including virtual training points to capture boundary conditions, and the significant loss of fidelity when training on stock-path-based datasets. Journal: Applied Mathematical Finance Pages: 330-360 Issue: 4 Volume: 28 Year: 2021 Month: 07 X-DOI: 10.1080/1350486X.2022.2039250 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2039250 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:4:p:330-360 Template-Type: ReDIF-Article 1.0 Author-Name: Marc Sabate Vidales Author-X-Name-First: Marc Author-X-Name-Last: Sabate Vidales Author-Name: David Šiška Author-X-Name-First: David Author-X-Name-Last: Šiška Author-Name: Lukasz Szpruch Author-X-Name-First: Lukasz Author-X-Name-Last: Szpruch Title: Unbiased Deep Solvers for Linear Parametric PDEs Abstract: We develop several deep learning algorithms for approximating families of parametric PDE solutions. The proposed algorithms approximate solutions together with their gradients, which in the context of mathematical finance means that the derivative prices and hedging strategies are computed simultaneously. Having approximated the gradient of the solution, one can combine it with a Monte Carlo simulation to remove the bias in the deep network approximation of the PDE solution (derivative price). This is achieved by leveraging the Martingale Representation Theorem and combining the Monte Carlo simulation with the neural network. The resulting algorithm is robust with respect to the quality of the neural network approximation and consequently can be used as a black box in case only limited a-priori information about the underlying problem is available. We believe this is important as neural network-based algorithms often require fair amount of tuning to produce satisfactory results. The methods are empirically shown to work for high-dimensional problems (e.g., 100 dimensions). We provide diagnostics that shed light on appropriate network architectures. Journal: Applied Mathematical Finance Pages: 299-329 Issue: 4 Volume: 28 Year: 2021 Month: 07 X-DOI: 10.1080/1350486X.2022.2030773 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2030773 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:4:p:299-329 Template-Type: ReDIF-Article 1.0 # input file: catalog-resolver-2565011781094273705.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220713T202513 git hash: 99d3863004 Author-Name: Jakob Albers Author-X-Name-First: Jakob Author-X-Name-Last: Albers Author-Name: Mihai Cucuringu Author-X-Name-First: Mihai Author-X-Name-Last: Cucuringu Author-Name: Sam Howison Author-X-Name-First: Sam Author-X-Name-Last: Howison Author-Name: Alexander Y. Shestopaloff Author-X-Name-First: Alexander Y. Author-X-Name-Last: Shestopaloff Title: Fragmentation, Price Formation and Cross-Impact in Bitcoin Markets Abstract: In the light of micro-scale inefficiencies due to the highly fragmented bitcoin trading landscape, we use a granular data set comprising orderbook and trades data from the most liquid bitcoin markets, to understand the price formation process at sub-1-second time scales. To this end, we construct a set of features that encapsulate relevant microstructural information over short lookback windows. These features are subsequently leveraged, first to generate a leader–lagger network that quantifies how markets impact one another, and then to train linear models capable of explaining between 10% and 37% of total variation in 500 ms future returns (depending on which market is the prediction target). The results are then compared with those of various PnL calculations that take trading realities, such as transaction costs, into account. The PnL calculations are based on natural taker strategies (meaning they employ market orders) associated with each model. Our findings emphasize the role of a market's fee regime in determining both its propensity to lead or lag, and the profitability of our taker strategy. We further derive a natural maker strategy (using only passive limit orders) which, due to the difficulties associated with backtesting maker strategies, we test in a real-world live trading experiment, in which we turned over 1.5 M USD in notional volume. Lending additional confidence to our models, and by extension to the features they are based on, the results indicate a significant improvement over a naive benchmark strategy, which we also deploy in a live trading environment with real capital, for the sake of comparison. Journal: Applied Mathematical Finance Pages: 395-448 Issue: 5 Volume: 28 Year: 2021 Month: 09 X-DOI: 10.1080/1350486X.2022.2080083 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2080083 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:5:p:395-448 Template-Type: ReDIF-Article 1.0 # input file: catalog-resolver6997315718562489314.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220713T202513 git hash: 99d3863004 Author-Name: Sébastien Bossu Author-X-Name-First: Sébastien Author-X-Name-Last: Bossu Title: Static Replication of European Multi-Asset Options with Homogeneous Payoff Abstract: The replication of any European contingent claim by a static continuous portfolio of calls and puts, formally proven by [Carr, Peter, and Dilip Madan. 1998. “Towards a Theory of Volatility Trading.” In Volatility: New Estimation Techniques for Pricing Derivatives, Vol. 29, edited by Robert A. Jarrow, 417–427. Risk books.] extends to multi-asset claims with absolutely homogeneous payoff. Using sophisticated tools from integral geometry, we show how such claims may be replicated with a continuum of vanilla basket calls and derive closed-form solutions to replicate two-asset best-of and worst-of options. We also derive a novel mathematical formula to invert the Radon transform which we apply to obtain a tractable expression of the joint implied distribution. Consequently, a large class of multi-asset options admit a model-free price enforced by arbitrage, just as single-asset European claims do. Journal: Applied Mathematical Finance Pages: 381-394 Issue: 5 Volume: 28 Year: 2021 Month: 09 X-DOI: 10.1080/1350486X.2022.2085122 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2085122 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:5:p:381-394 Template-Type: ReDIF-Article 1.0 # input file: catalog-resolver914888489498079041.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220713T202513 git hash: 99d3863004 Author-Name: Shuaiqiang Liu Author-X-Name-First: Shuaiqiang Author-X-Name-Last: Liu Author-Name: Álvaro Leitao Author-X-Name-First: Álvaro Author-X-Name-Last: Leitao Author-Name: Anastasia Borovykh Author-X-Name-First: Anastasia Author-X-Name-Last: Borovykh Author-Name: Cornelis W. Oosterlee Author-X-Name-First: Cornelis W. Author-X-Name-Last: Oosterlee Title: On a Neural Network to Extract Implied Information from American Options Abstract: Extracting implied information, like volatility and dividend, from observed option prices is a challenging task when dealing with American options, because of the complex-shaped early-exercise regions and the computational costs to solve the corresponding mathematical problem repeatedly. We will employ a data-driven machine learning approach to estimate the Black-Scholes implied volatility and the dividend yield for American options in a fast and robust way. To determine the implied volatility, the inverse function is approximated by an artificial neural network on the effective computational domain of interest, which decouples the offline (training) and online (prediction) stages and thus eliminates the need for an iterative process. In the case of an unknown dividend yield, we formulate the inverse problem as a calibration problem and determine simultaneously the implied volatility and dividend yield. For this, a generic and robust calibration framework, the Calibration Neural Network (CaNN), is introduced to estimate multiple parameters. It is shown that machine learning can be used as an efficient numerical technique to extract implied information from American options, particularly when considering multiple early-exercise regions due to negative interest rates. Journal: Applied Mathematical Finance Pages: 449-475 Issue: 5 Volume: 28 Year: 2021 Month: 09 X-DOI: 10.1080/1350486X.2022.2097099 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2097099 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:5:p:449-475 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2108858_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Sascha Desmettre Author-X-Name-First: Sascha Author-X-Name-Last: Desmettre Author-Name: Jörg Wenzel Author-X-Name-First: Jörg Author-X-Name-Last: Wenzel Title: On the Valuation of Discrete Asian Options in High Volatility Environments Abstract: In this paper, we are concerned with the Monte Carlo valuation of discretely sampled arithmetic and geometric average options in the Black-Scholes model and the stochastic volatility model of Heston in high volatility environments. To this end, we examine the limits and convergence rates of asset prices in these models when volatility parameters tend to infinity. We observe, on the one hand, that asset prices, as well as their arithmetic means converge to zero almost surely, while the respective expectations are constantly equal to the initial asset price. On the other hand, the expectation of geometric means of asset prices converges to zero. Moreover, we elaborate on the direct consequences for option prices based on such means and illustrate the implications of these findings for the design of efficient Monte-Carlo valuation algorithms. As a suitable control variate, we need among others the price of such discretely sampled geometric Asian options in the Heston model, for which we derive a closed-form solution. Journal: Applied Mathematical Finance Pages: 508-533 Issue: 6 Volume: 28 Year: 2021 Month: 11 X-DOI: 10.1080/1350486X.2022.2108858 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2108858 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:6:p:508-533 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2110130_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Peter Carr Author-X-Name-First: Peter Author-X-Name-Last: Carr Author-Name: Roger Lee Author-X-Name-First: Roger Author-X-Name-Last: Lee Author-Name: Matthew Lorig Author-X-Name-First: Matthew Author-X-Name-Last: Lorig Title: Semi-Robust Replication of Barrier-Style Claims on Price and Volatility Abstract: We show how to price and replicate a variety of barrier-style claims written on the log price X and quadratic variation $ \langle X\rangle $ 〈X〉 of a risky asset. Our framework assumes no arbitrage, frictionless markets and zero interest rates. We model the risky asset as a strictly positive continuous semimartingale with an independent volatility process. The volatility process may exhibit jumps and may be non-Markovian. As hedging instruments, we use only the underlying risky asset, zero-coupon bonds, and European calls and puts with the same maturity as the barrier-style claim. We consider knock-in, knock-out and rebate claims in single and double barrier varieties. Journal: Applied Mathematical Finance Pages: 534-559 Issue: 6 Volume: 28 Year: 2021 Month: 11 X-DOI: 10.1080/1350486X.2022.2110130 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2110130 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:6:p:534-559 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2101010_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Marcos Escobar-Anel Author-X-Name-First: Marcos Author-X-Name-Last: Escobar-Anel Author-Name: Ben Spies Author-X-Name-First: Ben Author-X-Name-Last: Spies Author-Name: Rudi Zagst Author-X-Name-First: Rudi Author-X-Name-Last: Zagst Title: Expected Utility Theory on General Affine GARCH Models Abstract: Expected utility theory has produced abundant analytical results in continuous-time finance, but with very little success for discrete-time models. Assuming the underlying asset price follows a general affine GARCH model which allows for non-Gaussian innovations, our work produces an approximate closed-form recursive representation for the optimal strategy under a constant relative risk aversion (CRRA) utility function. We provide conditions for optimality and demonstrate that the optimal wealth is also an affine GARCH. In particular, we fully develop the application to the IG-GARCH model hence accommodating negatively skewed and leptokurtic asset returns. Relying on two popular daily parametric estimations, our numerical analyses give a first window into the impact of the interaction of heteroscedasticity, skewness and kurtosis on optimal portfolio solutions. We find that losses arising from following Gaussian (suboptimal) strategies, or Merton's static solution, can be up to $ 2.5\% $ 2.5% and 5%, respectively, assuming low-risk aversion of the investor and using a five-years time horizon. Journal: Applied Mathematical Finance Pages: 477-507 Issue: 6 Volume: 28 Year: 2021 Month: 11 X-DOI: 10.1080/1350486X.2022.2101010 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2101010 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:28:y:2021:i:6:p:477-507 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2108857_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Tina T. Swan Author-X-Name-First: Tina T. Author-X-Name-Last: Swan Author-Name: Bruce Q. Swan Author-X-Name-First: Bruce Q. Author-X-Name-Last: Swan Author-Name: Xinfu Chen Author-X-Name-First: Xinfu Author-X-Name-Last: Chen Title: Pricing the Excess Volatility in Foreign Exchange Risk Premium and Forward Rate Bias Abstract: We present the pricing of the documented excess volatility of the foreign exchange risk premium, relative to the interest rate differential. By specifying a term structure of interest rate model, the physical probability measure along with the pricing kernels or discount factors are used to derive a system for the expected future spot rate and the forward rate. The theoretical loads are found by solving the Riccati ordinary differential equations, and dynamic factors are captured to set up the global factors for both currencies. It shows that we prove the interest-rate surfaces are almost identical to the empirical ones, and the theoretical interest rates are guaranteed to be positive. Journal: Applied Mathematical Finance Pages: 33-61 Issue: 1 Volume: 29 Year: 2022 Month: 01 X-DOI: 10.1080/1350486X.2022.2108857 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2108857 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:1:p:33-61 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2125885_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Carol Alexander Author-X-Name-First: Carol Author-X-Name-Last: Alexander Author-Name: Daniel F. Heck Author-X-Name-First: Daniel F. Author-X-Name-Last: Heck Author-Name: Andreas Kaeck Author-X-Name-First: Andreas Author-X-Name-Last: Kaeck Title: The Role of Binance in Bitcoin Volatility Transmission Abstract: We analyse high-frequency realized volatility dynamics and spillovers between centralized crypto exchanges that offer spot and derivative contracts for bitcoin against the US dollar or the stable coin tether. The tether-margined perpetual contract on Binance is clearly the main source of volatility, continuously transmitting strong flows to all other instruments and receiving very little volatility from other sources. We also find that crypto exchanges exhibit much higher interconnectedness when traditional Western stock markets are open. Especially during the US time zone, volatility outflows from Binance are much higher than at other times, and Bitcoin traders are more attentive and reactive to prevailing market conditions. Our results highlight that market regulators should pay more attention to the tether-margined derivatives products available on most self-regulated exchanges, most importantly on Binance. Journal: Applied Mathematical Finance Pages: 1-32 Issue: 1 Volume: 29 Year: 2022 Month: 01 X-DOI: 10.1080/1350486X.2022.2125885 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2125885 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:1:p:1-32 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2136727_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Philippe Casgrain Author-X-Name-First: Philippe Author-X-Name-Last: Casgrain Author-Name: Brian Ning Author-X-Name-First: Brian Author-X-Name-Last: Ning Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Deep Q-Learning for Nash Equilibria: Nash-DQN Abstract: Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data-efficient Deep-Q-learning methodology for model-free learning of Nash equilibria for general-sum stochastic games. The algorithm uses a locally linear-quadratic expansion of the stochastic game, which leads to analytically solvable optimal actions. The expansion is parametrized by deep neural networks to give it sufficient flexibility to learn the environment without the need to experience all state-action pairs. We study symmetry properties of the algorithm stemming from label-invariant stochastic games and as a proof of concept, apply our algorithm to learning optimal trading strategies in competitive electronic markets. Journal: Applied Mathematical Finance Pages: 62-78 Issue: 1 Volume: 29 Year: 2022 Month: 01 X-DOI: 10.1080/1350486X.2022.2136727 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2136727 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:1:p:62-78 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2154682_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Martin Redmann Author-X-Name-First: Martin Author-X-Name-Last: Redmann Title: Solving High-Dimensional Optimal Stopping Problems Using Optimization Based Model Order Reduction Abstract: Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from the curse of dimensionality. Therefore, the objective of this paper is to establish dimension reduction schemes for large-scale asset price models and to solve related optimal stopping problems (e.g., Bermudan option pricing) in the reduced setting, where regression is feasible. The proposed algorithm is based on an error measure between linear stochastic differential equations. We establish optimality conditions for this error measure with respect to the reduced system coefficients and propose a particular method that satisfies these conditions up to a small deviation. We illustrate the benefit of our approach in several numerical experiments, in which Bermudan option prices are determined. Journal: Applied Mathematical Finance Pages: 110-140 Issue: 2 Volume: 29 Year: 2022 Month: 03 X-DOI: 10.1080/1350486X.2022.2154682 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2154682 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:2:p:110-140 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2156900_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: J. H. Hoencamp Author-X-Name-First: J. H. Author-X-Name-Last: Hoencamp Author-Name: J. P. de Kort Author-X-Name-First: J. P. Author-X-Name-Last: de Kort Author-Name: B. D. Kandhai Author-X-Name-First: B. D. Author-X-Name-Last: Kandhai Title: The Impact of Stochastic Volatility on Initial Margin and MVA for Interest Rate Derivatives Abstract: In this research we investigate the impact of stochastic volatility on future initial margin (IM) and margin valuation adjustment (MVA) calculations for interest rate derivatives. An analysis is performed under different market conditions, namely during the peak of the Covid-19 crisis when the markets were stressed and during Q4 of 2020 when volatilities were low. The Cheyette short-rate model is extended by adding a stochastic volatility component, which is calibrated to fit the EUR swaption volatility surfaces. We incorporate the latest risk-free rate benchmarks (RFR), which in certain markets have been selected to replace the IBOR index. We extend modern Fourier pricing techniques to accommodate the RFR benchmark and derive closed-form sensitivity expressions, which are used to model IM profiles in a Monte Carlo simulation framework. The various results are compared to the deterministic volatility case. The results reveal that the inclusion of a stochastic volatility component can have a considerable impact on nonlinear derivatives, especially for far out-of-the-money swaptions. The effect is particularly pronounced if the market exhibits a substantial skew or smile in the implied volatility curve. This can have severe consequences for funding cost valuation and risk management. Journal: Applied Mathematical Finance Pages: 141-179 Issue: 2 Volume: 29 Year: 2022 Month: 03 X-DOI: 10.1080/1350486X.2022.2156900 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2156900 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:2:p:141-179 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2148115_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Max O. Souza Author-X-Name-First: Max O. Author-X-Name-Last: Souza Author-Name: Y. Thamsten Author-X-Name-First: Y. Author-X-Name-Last: Thamsten Title: On Regularized Optimal Execution Problems and Their Singular Limits Abstract: We investigate the portfolio execution problem under a framework in which volatility and liquidity are both uncertain. In our model, we assume that a multidimensional Markovian stochastic factor drives both of them. Moreover, we model indirect liquidity costs as temporary price impact, stipulating a power law to relate it to the agent's turnover rate. We first analyse the regularized setting, in which the admissible strategies do not ensure complete execution of the initial inventory. We prove the existence and uniqueness of a continuous and bounded viscosity solution of the Hamilton–Jacobi–Bellman equation, whence we obtain a characterization of the optimal trading rate. As a byproduct of our proof, we obtain a numerical algorithm. Then, we analyse the constrained problem, in which admissible strategies must guarantee complete execution to the trader. We solve it through a monotonicity argument, obtaining the optimal strategy as a singular limit of the regularized counterparts. Journal: Applied Mathematical Finance Pages: 79-109 Issue: 2 Volume: 29 Year: 2022 Month: 03 X-DOI: 10.1080/1350486X.2022.2148115 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2148115 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:2:p:79-109 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2125884_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Bartosz Jaroszkowski Author-X-Name-First: Bartosz Author-X-Name-Last: Jaroszkowski Author-Name: Max Jensen Author-X-Name-First: Max Author-X-Name-Last: Jensen Title: Valuation of European Options Under an Uncertain Market Price of Volatility Risk Abstract: We propose a model to quantify the effect of parameter uncertainty on the option price in the Heston model. More precisely, we present a Hamilton–Jacobi–Bellman framework which allows us to evaluate best and worst-case scenarios under an uncertain market price of volatility risk. For the numerical approximation, the Hamilton–Jacobi–Bellman equation is reformulated to enable the solution with a finite element method. A case study with butterfly options exhibits how the dependence of Delta on the magnitude of the uncertainty is nonlinear and highly varied across the parameter regime. Journal: Applied Mathematical Finance Pages: 213-226 Issue: 3 Volume: 29 Year: 2022 Month: 05 X-DOI: 10.1080/1350486X.2022.2125884 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2125884 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:3:p:213-226 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2161588_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20220907T060133 git hash: 85d61bd949 Author-Name: Ryan Donnelly Author-X-Name-First: Ryan Author-X-Name-Last: Donnelly Title: Optimal Execution: A Review Abstract: This review article is intended to collect and summarize many of the results in the field of optimal execution over the last twenty years. In doing so, we describe the general workings of the limit order book so that the sources of costs and risks which need to be optimized are understood. The initial models considered propose simple dynamics for prices which allow easily computable strategies which maximize risk-adjusted profits. Subsequently, the review is divided into two major parts. The first explores several works which investigate how optimal liquidation strategies are modified to account for more complex dynamics, namely other stochastic or non-linear factors. The second presents optimal trading strategies when the agent utilizes benchmarks in addition to risk-adjusted wealth, or when she has objectives beyond optimal liquidation. Journal: Applied Mathematical Finance Pages: 181-212 Issue: 3 Volume: 29 Year: 2022 Month: 05 X-DOI: 10.1080/1350486X.2022.2161588 File-URL: http://hdl.handle.net/10.1080/1350486X.2022.2161588 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:3:p:181-212 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2194658_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Giuliana Bordigoni Author-X-Name-First: Giuliana Author-X-Name-Last: Bordigoni Author-Name: Alessio Figalli Author-X-Name-First: Alessio Author-X-Name-Last: Figalli Author-Name: Anthony Ledford Author-X-Name-First: Anthony Author-X-Name-Last: Ledford Author-Name: Philipp Ustinov Author-X-Name-First: Philipp Author-X-Name-Last: Ustinov Title: Strategic Execution Trajectories Abstract: We obtain the optimal execution strategy for two sequential trades in the presence of a transient price impact. We first present a novel and general solution method for the case of a single trade (a metaorder) that is executed as a sequence of sub-trades (child orders). We then analyze the case of two sequential metaorders, including the case where the size and direction of the second metaorder are uncertain at the time the first metaorder is initiated. We obtain the optimal execution strategy under two different cost functions. First, we minimize the total cost when each metaorder is benchmarked to the price at its initiation, the total separate costs approach widely used by practitioners. Although simple, we show that optimizing total separate costs can lead to a significant understatement of the real costs of trading whilst also adversely impacting order scheduling. We overcome these issues by introducing a new cost function that splits the second metaorder into two parts, one that is predictable when the first metaorder is initiated and a residual that is not. The predictable and residual parts of the second metaorder are benchmarked using the initiation prices of the first and second metaorders, respectively. We prove existence of an optimal execution trajectory for linear instantaneous price impact and positive definite decay, and derive the explicit form of the minimizer in the special case of exponentially decaying impact, however uniqueness in general remains unproven. Various numerical examples are included for illustration. Journal: Applied Mathematical Finance Pages: 288-330 Issue: 4 Volume: 29 Year: 2022 Month: 07 X-DOI: 10.1080/1350486X.2023.2194658 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2194658 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:4:p:288-330 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2180399_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Thomas Deschatre Author-X-Name-First: Thomas Author-X-Name-Last: Deschatre Author-Name: Pierre Gruet Author-X-Name-First: Pierre Author-X-Name-Last: Gruet Title: Electricity Intraday Price Modelling with Marked Hawkes Processes Abstract: We consider a two-dimensional marked Hawkes process with increasing baseline intensity to model prices on electricity intraday markets. This model allows to represent different empirical facts such as increasing market activity, random jump sizes but above all microstructure noise through the signature plot. This last feature is of particular importance for practitioners and has not yet been modelled on those particular markets. We provide analytic formulas for first and second moments and for the signature plot, extending the classic results of Bacry et al. [2013a. ‘Modelling Microstructure Noise with Mutually Exciting Point Processes.’ Quantitative Finance 13 (1): 65–77. doi:10.1080/14697688.2011.647054.] in the context of Hawkes processes with random jump sizes and time-dependent baseline intensity. The tractable model we propose is estimated on German data and seems to fit the data well. We also provide a result about the convergence of the price process to a Brownian motion with increasing volatility at macroscopic scales, highlighting the Samuelson effect. Journal: Applied Mathematical Finance Pages: 227-260 Issue: 4 Volume: 29 Year: 2022 Month: 07 X-DOI: 10.1080/1350486X.2023.2180399 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2180399 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:4:p:227-260 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2193343_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: René Carmona Author-X-Name-First: René Author-X-Name-Last: Carmona Author-Name: Claire Zeng Author-X-Name-First: Claire Author-X-Name-Last: Zeng Title: Optimal Execution with Identity Optionality Abstract: This paper investigates the impact of anonymous trading on the agents' strategy in an optimal execution framework. It mainly explores the specificity of order attribution on the Toronto Stock Exchange, where brokers can choose to either trade with their own identity or under a generic anonymous code that is common to all the brokers. We formulate a stochastic differential game for the optimal execution problem of a population of N brokers and incorporate permanent and temporary price impacts for both the identity-revealed and anonymous trading processes. We then formulate the limiting mean-field game of controls with common noise and obtain a solution in closed-form via the probablistic approach for the Almgren-Chris price impact framework. Finally, we perform a sensitivity analysis to explore the impact of the model parameters on the optimal strategy. Journal: Applied Mathematical Finance Pages: 261-287 Issue: 4 Volume: 29 Year: 2022 Month: 07 X-DOI: 10.1080/1350486X.2023.2193343 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2193343 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:4:p:261-287 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2224354_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Peter A. Forsyth Author-X-Name-First: Peter A. Author-X-Name-Last: Forsyth Author-Name: Kenneth R. Vetzal Author-X-Name-First: Kenneth R. Author-X-Name-Last: Vetzal Title: Multi-Period Mean Expected-Shortfall Strategies: ‘Cut Your Losses and Ride Your Gains’ Abstract: Dynamic mean-variance (MV) optimal strategies are inherently contrarian. Following periods of strong equity returns, there is a tendency to de-risk the portfolio by shifting into risk-free investments. On the other hand, if the portfolio still has some equity exposure, the weight on equities will increase following stretches of poor equity returns. This is essentially due to using variance as a risk measure, which penalizes both upside and downside deviations relative to a satiation point. As an alternative, we propose a dynamic trading strategy based on an expected wealth (EW), expected shortfall (ES) objective function. ES is defined as the mean of the worst β fraction of the outcomes, hence the EW-ES objective directly targets left tail risk. We use stochastic control methods to determine the optimal trading strategy. Our numerical method allows us to impose realistic constraints: no leverage, no shorting, infrequent rebalancing. For 5 year investment horizons, this strategy generates an annualized alpha of 180 bps compared to a 60:40 stock-bond constant weight policy. Bootstrap resampling with historical data shows that these results are robust to parametric model misspecification. The optimal EW-ES strategy is generally a momentum-type policy, in contrast to the contrarian MV optimal strategy. Journal: Applied Mathematical Finance Pages: 402-438 Issue: 5 Volume: 29 Year: 2022 Month: 09 X-DOI: 10.1080/1350486X.2023.2224354 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2224354 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:5:p:402-438 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2221448_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Samuel N. Cohen Author-X-Name-First: Samuel N. Author-X-Name-Last: Cohen Author-Name: Christoph Reisinger Author-X-Name-First: Christoph Author-X-Name-Last: Reisinger Author-Name: Sheng Wang Author-X-Name-First: Sheng Author-X-Name-Last: Wang Title: Hedging Option Books Using Neural-SDE Market Models Abstract: We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimum-variance-based hedging strategies using these models and examine their performance when applied to various option portfolios using real-world data. Through backtesting analysis over typical and stressed market periods, we show that neural-SDE market models achieve lower hedging errors than Black–Scholes delta and delta-vega hedging consistently over time, and are less sensitive to the tenor choice of hedging instruments. In addition, hedging using market models leads to similar performance to hedging using Heston models, while the former tends to be more robust during stressed market periods. Journal: Applied Mathematical Finance Pages: 366-401 Issue: 5 Volume: 29 Year: 2022 Month: 09 X-DOI: 10.1080/1350486X.2023.2221448 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2221448 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:5:p:366-401 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2210290_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Nikhil Krishnan Author-X-Name-First: Nikhil Author-X-Name-Last: Krishnan Author-Name: Ronnie Sircar Author-X-Name-First: Ronnie Author-X-Name-Last: Sircar Title: Accelerated Share Repurchases Under Stochastic Volatility Abstract: Accelerated share repurchases (ASRs) are a type of stock buyback wherein the repurchasing firm contracts a financial intermediary to acquire the shares on its behalf. The intermediary purchases the shares from the open market and is compensated by the firm according to the average of the stock price over the repurchasing interval, whose end can be chosen by the intermediary. Hence, the intermediary needs to decide both how to minimize the cost of acquiring the shares, and when to exercise its contract to maximize its payment. Studies of ASRs typically assume a constant volatility, but the longer time horizon of ASRs, on the order of months, indicates that the variation of the volatility should be considered. We analyze the optimal strategy of the intermediary within the continuous-time framework of the Heston model for the evolution of the stock price and volatility, which is described by a free-boundary problem which we derive here. To solve this system numerically, we make use of deep learning. Through simulations, we find that the intermediary can acquire shares at lower cost and lower risk if it takes into account the stochasticity of the volatility. Journal: Applied Mathematical Finance Pages: 331-365 Issue: 5 Volume: 29 Year: 2022 Month: 09 X-DOI: 10.1080/1350486X.2023.2210290 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2210290 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:5:p:331-365 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2248791_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Matteo Gardini Author-X-Name-First: Matteo Author-X-Name-Last: Gardini Author-Name: Piergiacomo Sabino Author-X-Name-First: Piergiacomo Author-X-Name-Last: Sabino Title: Exchange Option Pricing Under Variance Gamma-Like Models Abstract: In this article, we focus on the pricing of exchange options when the risk-neutral dynamic of log-prices follows either the well-known variance gamma or the recent variance gamma++ process introduced in Gardini et al. (2022. “The Variance Gamma++ Process and Applications to Energy Markets.” Applied Stochastic Models in Business and Industry 38 (2): 391–418. https://doi.org/10.1002/asmb.v38.2.). In particular, for the former model we can derive a Margrabe's type formula whereas for the latter one we can write an ‘integral free’ formula. Furthermore, we show how to construct a general multidimensional versions of the variance gamma++ processes preserving both the mathematical and numerical tractabilities. Finally we apply the derived models to German and French energy power markets: we calibrate their parameters using real market data and we accordingly evaluate exchange options with the derived closed formulas, Fourier based methods and Monte Carlo techniques. Journal: Applied Mathematical Finance Pages: 494-521 Issue: 6 Volume: 29 Year: 2022 Month: 11 X-DOI: 10.1080/1350486X.2023.2248791 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2248791 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:6:p:494-521 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2241130_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Fayçal Drissi Author-X-Name-First: Fayçal Author-X-Name-Last: Drissi Title: Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals Abstract: We study a differential Riccati equation (DRE) with indefinite matrix coefficients, which arises in a wide class of practical problems. We show that the DRE solves an associated control problem, which is key to provide existence and uniqueness of a solution. As an application, we solve two algorithmic trading problems in which the agent adopts a constant absolute risk-aversion (CARA) utility function, and where the optimal strategies use signals and past observations of prices to improve their performance. First, we derive a multi-asset market making strategy in over-the-counter markets, where the market maker uses an external trading venue to hedge risk. Second, we derive an optimal trading strategy that uses prices and signals to learn the drift in the asset prices. Journal: Applied Mathematical Finance Pages: 457-493 Issue: 6 Volume: 29 Year: 2022 Month: 11 X-DOI: 10.1080/1350486X.2023.2241130 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2241130 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:6:p:457-493 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2239850_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Mohamed Hamdouche Author-X-Name-First: Mohamed Author-X-Name-Last: Hamdouche Author-Name: Pierre Henry-Labordere Author-X-Name-First: Pierre Author-X-Name-Last: Henry-Labordere Author-Name: Huyên Pham Author-X-Name-First: Huyên Author-X-Name-Last: Pham Title: Policy Gradient Learning Methods for Stochastic Control with Exit Time and Applications to Share Repurchase Pricing Abstract: We develop policy gradients methods for stochastic control with exit time in a model-free setting. We propose two types of algorithms for learning either directly the optimal policy or by learning alternately the value function (critic) and the optimal control (actor). The use of randomized policies is crucial for overcoming notably the issue related to the exit time in the gradient computation. We demonstrate the effectiveness of our approach by implementing our numerical schemes in the application to the problem of share repurchase pricing. Our results show that the proposed policy gradient methods outperform PDE or other neural networks techniques in a model-based setting. Furthermore, our algorithms are flexible enough to incorporate realistic market conditions like, e.g., price impact or transaction costs. Journal: Applied Mathematical Finance Pages: 439-456 Issue: 6 Volume: 29 Year: 2022 Month: 11 X-DOI: 10.1080/1350486X.2023.2239850 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2239850 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:29:y:2022:i:6:p:439-456 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2257217_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Samuel N. Cohen Author-X-Name-First: Samuel N. Author-X-Name-Last: Cohen Author-Name: Christoph Reisinger Author-X-Name-First: Christoph Author-X-Name-Last: Reisinger Author-Name: Sheng Wang Author-X-Name-First: Sheng Author-X-Name-Last: Wang Title: Arbitrage-Free Neural-SDE Market Models Abstract: Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting underlying financial constraints and while being practically implementable. We derive a state space for prices which are free from static (or model-independent) arbitrage and study the inference problem where a model is learnt from discrete time series data of stock and option prices. We use neural networks as function approximators for the drift and diffusion of the modelled SDE system, and impose constraints on the neural nets such that no-arbitrage conditions are preserved. In particular, we give methods to calibrate neural SDE models which are guaranteed to satisfy a set of linear inequalities. We validate our approach with numerical experiments using data generated from a Heston stochastic local volatility model. Journal: Applied Mathematical Finance Pages: 1-46 Issue: 1 Volume: 30 Year: 2023 Month: 01 X-DOI: 10.1080/1350486X.2023.2257217 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2257217 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:1:p:1-46 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2261459_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Elisa Alòs Author-X-Name-First: Elisa Author-X-Name-Last: Alòs Author-Name: David García-Lorite Author-X-Name-First: David Author-X-Name-Last: García-Lorite Author-Name: Makar Pravosud Author-X-Name-First: Makar Author-X-Name-Last: Pravosud Title: On the Skew and Curvature of the Implied and Local Volatilities Abstract: In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $ \frac {1}{H+3/2} $ 1H+3/2 rule (where H denotes the Hurst parameter of the volatility process) for rough volatilities (see F. Bourgey, S. De Marco, P. Friz, and P. Pigato. 2022. “Local Volatility under Rough Volatility.” arXiv:2204.02376v1 [q-fin.MF] https://doi.org/10.48550/arXiv.2204.02376.), that states that the short-time skew slope of the at-the-money implied volatility is $ \frac {1}{H+3/2} $ 1H+3/2 of the corresponding slope for local volatilities. Moreover, we see that the at-the-money short-end curvature of the implied volatility can be written in terms of the short-end skew and curvature of the local volatility and vice versa. Additionally, this relationship depends on H. Journal: Applied Mathematical Finance Pages: 47-67 Issue: 1 Volume: 30 Year: 2023 Month: 01 X-DOI: 10.1080/1350486X.2023.2261459 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2261459 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:1:p:47-67 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2277957_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Álvaro Cartea Author-X-Name-First: Álvaro Author-X-Name-Last: Cartea Author-Name: Fayçal Drissi Author-X-Name-First: Fayçal Author-X-Name-Last: Drissi Author-Name: Marcello Monga Author-X-Name-First: Marcello Author-X-Name-Last: Monga Title: Predictable Losses of Liquidity Provision in Constant Function Markets and Concentrated Liquidity Markets Abstract: We introduce a new comprehensive and model-free measure for the unhedgeable and predictable loss (PL) incurred by liquidity providers (LPs) in constant function markets (CFMs) and in concentrated liquidity markets. PL compares the value of the LP's holdings in the CFM liquidity pool (assuming no fee revenue) with that of a self-financing portfolio that (i) continuously replicates the dynamic holdings of the LP in the pool to offset the market risk of the LP's position, and (ii) invests in a risk-free account. We provide closed-form formulae for PL in CFMs with and without concentrated liquidity, and show that the losses stem from two sources: convexity cost, which depends on liquidity taking activity and the convexity of the pool's trading function; and opportunity cost, which is due to locking the LP's assets in the pool. For liquidity providers, PL is the appropriate measure to assess the cost of liquidity provision in CFMs, so that fees and compensation to LPs provide the right incentives for a well-functioning market. When prices form outside of the pool, we show that PL is reduced when liquidity taking is costly, i.e., when the convexity of the pool's trading function is high. On the other hand, when prices form in the pool, PL is reduced when liquidity taking is cheap, i.e., when the convexity of the trading function is low. Finally, we use Uniswap v3 and Binance transaction data to compute PL and fees collected by LPs and show that, at present, liquidity provision in CFMs is a loss-leading activity. Journal: Applied Mathematical Finance Pages: 69-93 Issue: 2 Volume: 30 Year: 2023 Month: 03 X-DOI: 10.1080/1350486X.2023.2277957 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2277957 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:2:p:69-93 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2277960_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20230119T200553 git hash: 724830af20 Author-Name: Rama Cont Author-X-Name-First: Rama Author-X-Name-Last: Cont Author-Name: Milena Vuletić Author-X-Name-First: Milena Author-X-Name-Last: Vuletić Title: Simulation of Arbitrage-Free Implied Volatility Surfaces Abstract: We present a computationally tractable method for simulating arbitrage-free implied volatility surfaces. We illustrate how our method may be combined with a data-driven model based on historical SPX implied volatility data to generate dynamic scenarios for arbitrage-free implied volatility surfaces. Our approach conciliates static arbitrage constraints with a realistic representation of statistical properties of implied volatility co-movements. Journal: Applied Mathematical Finance Pages: 94-121 Issue: 2 Volume: 30 Year: 2023 Month: 03 X-DOI: 10.1080/1350486X.2023.2277960 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2277960 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:2:p:94-121 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2299467_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: Giacomo Giorgio Author-X-Name-First: Giacomo Author-X-Name-Last: Giorgio Author-Name: Barbara Pacchiarotti Author-X-Name-First: Barbara Author-X-Name-Last: Pacchiarotti Author-Name: Paolo Pigato Author-X-Name-First: Paolo Author-X-Name-Last: Pigato Title: Short-Time Asymptotics for Non-Self-Similar Stochastic Volatility Models Abstract: We provide a short-time large deviation principle (LDP) for stochastic volatility models, where the volatility is expressed as a function of a Volterra process. This LDP does not require strict self-similarity assumptions on the Volterra process. For this reason, we are able to apply such an LDP to two notable examples of non-self-similar rough volatility models: models where the volatility is given as a function of a log-modulated fractional Brownian motion (Bayer, C., F. Harang, and P. Pigato. 2021. “Log-Modulated Rough Stochastic Volatility Models.” SIAM Journal on Financial Mathematics 12 (3): 1257–1284), and models where it is given as a function of a fractional Ornstein–Uhlenbeck (fOU) process (Gatheral, J., T. Jaisson, and M. Rosenbaum. 2018. “Volatility is Rough.” Quantitative Finance 18 (6): 933–949). In both cases, we derive consequences for short-maturity European option prices implied volatility surfaces and implied volatility skew. In the fOU case, we also discuss moderate deviations pricing and simulation results. Journal: Applied Mathematical Finance Pages: 123-152 Issue: 3 Volume: 30 Year: 2023 Month: 05 X-DOI: 10.1080/1350486X.2023.2299467 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2299467 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:3:p:123-152 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2301354_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20231214T103247 git hash: d7a2cb0857 Author-Name: David Wu Author-X-Name-First: David Author-X-Name-Last: Wu Author-Name: Sebastian Jaimungal Author-X-Name-First: Sebastian Author-X-Name-Last: Jaimungal Title: Robust Risk-Aware Option Hedging Abstract: The objectives of option hedging/trading extend beyond mere protection against downside risks, with a desire to seek gains also driving agent's strategies. In this study, we showcase the potential of robust risk-aware reinforcement learning (RL) in mitigating the risks associated with path-dependent financial derivatives. We accomplish this by leveraging a policy gradient approach that optimizes robust risk-aware performance criteria. We specifically apply this methodology to the hedging of barrier options, and highlight how the optimal hedging strategy undergoes distortions as the agent moves from being risk-averse to risk-seeking. As well as how the agent robustifies their strategy. We further investigate the performance of the hedge when the data generating process (DGP) varies from the training DGP, and demonstrate that the robust strategies outperform the non-robust ones. Journal: Applied Mathematical Finance Pages: 153-174 Issue: 3 Volume: 30 Year: 2023 Month: 05 X-DOI: 10.1080/1350486X.2023.2301354 File-URL: http://hdl.handle.net/10.1080/1350486X.2023.2301354 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:3:p:153-174 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2316139_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Tim Leung Author-X-Name-First: Tim Author-X-Name-Last: Leung Author-Name: Kevin W. Lu Author-X-Name-First: Kevin W. Author-X-Name-Last: Lu Title: Monte Carlo Simulation for Trading Under a Lévy-Driven Mean-Reverting Framework Abstract: We present a Monte Carlo approach to pairs trading on mean-reverting spreads modelled by Lévy-driven Ornstein-Uhlenbeck processes. Specifically, we focus on using a variance gamma driving process, an infinite activity pure jump process to allow for more flexible models of the price spread than is available in the classical model. However, this generalization comes at the cost of not having analytic formulas, so we apply Monte Carlo methods to determine optimal trading levels and develop a variance reduction technique using control variates. Within this framework, we numerically examine how the optimal trading strategies are affected by the parameters of the model. In addition, we extend our method to bivariate spreads modelled using a weak variance alpha-gamma driving process, and explore the effect of correlation on these trades. Journal: Applied Mathematical Finance Pages: 207-230 Issue: 4 Volume: 30 Year: 2023 Month: 07 X-DOI: 10.1080/1350486X.2024.2316139 File-URL: http://hdl.handle.net/10.1080/1350486X.2024.2316139 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:4:p:207-230 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2303078_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Claudio Bellani Author-X-Name-First: Claudio Author-X-Name-Last: Bellani Author-Name: Damiano Brigo Author-X-Name-First: Damiano Author-X-Name-Last: Brigo Author-Name: Mikko S. Pakkanen Author-X-Name-First: Mikko S. Author-X-Name-Last: Pakkanen Author-Name: Leandro Sánchez-Betancourt Author-X-Name-First: Leandro Author-X-Name-Last: Sánchez-Betancourt Title: Price Impact Without Averaging Abstract: We present a method to estimate price impact in order-driven markets that does not require averaging over executions or scenarios. Given order book data associated with one single execution of a sell metaorder, we estimate its contribution to price decrease during the trade. We do so by modelling the limit order book using a state-dependent Hawkes process, and by defining the price impact profile of the execution as a function of the compensator of the state-dependent Hawkes process. We apply our method to a dataset from NASDAQ, and we conclude that the scheduling of sell child orders has a bigger impact on price than their sizes. Journal: Applied Mathematical Finance Pages: 175-206 Issue: 4 Volume: 30 Year: 2023 Month: 07 X-DOI: 10.1080/1350486X.2024.2303078 File-URL: http://hdl.handle.net/10.1080/1350486X.2024.2303078 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:4:p:175-206 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2320339_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Alejandro Balbás Author-X-Name-First: Alejandro Author-X-Name-Last: Balbás Author-Name: Beatriz Balbás Author-X-Name-First: Beatriz Author-X-Name-Last: Balbás Author-Name: Raquel Balbás Author-X-Name-First: Raquel Author-X-Name-Last: Balbás Title: Buy and Hold Golden Strategies in Financial Markets with Frictions and Depth Constraints Abstract: This paper deals with coherent risk measures and golden strategies, that is, financial portfolios (or financial strategies) with a negative risk and a non positive price. Golden strategies are important because they enable us to outperform every portfolio in a return/risk approach. In fact, every portfolio of securities is beaten by adding the golden strategy, i.e., the portfolio plus the golden strategy is better than the portfolio alone. Computationally tractable algorithms will be presented, and the general framework will be very realistic. Indeed, the study will incorporate all the classical frictions provoked by the order book of a financial market, and it will be both buy-and-hold and model-free. Numerical experiments involving derivative markets will be analysed. Journal: Applied Mathematical Finance Pages: 231-248 Issue: 5 Volume: 30 Year: 2023 Month: 09 X-DOI: 10.1080/1350486X.2024.2320339 File-URL: http://hdl.handle.net/10.1080/1350486X.2024.2320339 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:5:p:231-248 Template-Type: ReDIF-Article 1.0 # input file: RAMF_A_2346478_J.xml processed with: repec_from_jats12.xsl darts-xml-transformations-20240209T083504 git hash: db97ba8e3a Author-Name: Elisa Alòs Author-X-Name-First: Elisa Author-X-Name-Last: Alòs Author-Name: Eulalia Nualart Author-X-Name-First: Eulalia Author-X-Name-Last: Nualart Author-Name: Makar Pravosud Author-X-Name-First: Makar Author-X-Name-Last: Pravosud Title: On the Implied Volatility of Asian Options Under Stochastic Volatility Models Abstract: In this paper, we study the short-time behaviour of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black–Scholes model with a general stochastic volatility process. Using techniques of the Malliavin calculus developed in Alòs, García-Lorite, and Muguruza [2022. On Smile Properties of Volatility Derivatives: Understanding the VIX Skew. SIAM Journal on Financial Mathematics. 13(1): 32–69. https://doi.org/10.1137/19M1269981], we give sufficient conditions on the stochastic volatility in order to compute the level of the implied volatility of the option when the maturity converges to zero. Then, we find a short maturity asymptotic formula for the skew slope of the implied volatility that depends on the correlation between prices and volatilities and the Hurst parameter of the volatility model. We apply our general results to the SABR and fractional Bergomi models, and provide numerical simulations that confirm the accurateness of the asymptotic formulas. Journal: Applied Mathematical Finance Pages: 249-274 Issue: 5 Volume: 30 Year: 2023 Month: 09 X-DOI: 10.1080/1350486X.2024.2346478 File-URL: http://hdl.handle.net/10.1080/1350486X.2024.2346478 File-Format: text/html File-Restriction: Access to full text is restricted to subscribers. Handle: RePEc:taf:apmtfi:v:30:y:2023:i:5:p:249-274