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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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