+-------+ ----+ Title +------------------------------------------------------------
bsopm - Black-Scholes European Option Pricing Model
+-------------------+ ----+ Table of Contents +------------------------------------------------
Syntax Options Description References
*** Examples
Author
+--------+ ----+ Syntax +-----------------------------------------------------------
bsopm Stock_Price Strike_Price , ir(var) Sigma(var) Time(var)
+---------+ ----+ Options +----------------------------------------------------------
ir(var) Interest Rate sigma(var) Standard Deviation = Volatility time(var) Expiration Time
+-------------+ ----+ Description +------------------------------------------------------
bsopm computes Black-Scholes European Option Pricing Model.
Fischer Black & Myron Scholes are 2 economist, who in 1973 published a paper which redefined finance and derivatives, with "The Pricing of Options & Corporate Liabilities" featured in the Journal of Political Economy in May of that year. The piece is arguably one of the most important papers within finance theory to date and allows us to price various derivatives, including options on commodities, financial assets and even pricing of employee stock options.
Assumptions of Black-Scholes Option Pricing: 1. No dividends are paid out on the underlying stock during the option > life. 2. The option can only be exercised at expiry (European characteristics > ) 3. Efficient markets (Market movements cannot be predicted) 4. Commissions are non-existent 5. Interest rates do not change over the life of the option (and are kn > own) 6. Stock returns follow a lognormal distribution.
European Options Pricing: are options which are only exercisable on the expiry date of the option and are valued using the Black Scholes option pricing forumla. There are only five inputs to the classic Black Scholes model: spot price, strike price, time until expiry, interest rate, and volatility. As such European options are typically the simplest options to value The dividend or yield on the underlying asset can also be an input on some extentions of the model. In contrast American Options can be exercised at any time up until and including the expiry date of the option.
The term European is confined to describing the exercise feature of the option (ie exercisable only on the expiry date) and is does not describe the geographic region of the underlying asset. For example, a European Option can be issued on a stock of a company listed on an Asian exchange.
Spot Price: The market price of the underlying asset on the valuation date. This can be a difficult input to estimate for options on illiquid assets, however under normal circumstances the closing market price can usually be used.
Strike Price: The price level at which the option holder has the right to buy or sell the underlying asset. It is the most straightforward input as it will always be given in the option contract.
Time to Maturity: Time (in years) until the option expires and the holder is no longer entitled to exercise the option.
Interest Rate: Risk free interest rate for the period until the option expires. The risk free rate should typically be a zero coupon government bond yield.
Volatility: Probably the most important single input to any option pricing model.
Implied Volatility: The volatility implied by the market price of traded options. As the price is already known and the volatility (which is typically an input) is unknown the pricing model is reversed to determine the volatility. When using the implied volatility it is important to be aware of the volatility surface. The volatility surface is the 3 dimensional representation of the relationship between volatility, option life and exercise price. Thus to use implied volatility the option from which the volatility is implied should have a similar life and exercise price (or ratio of market price to exercise price) as the option being valued.
+------------+ ----+ References +-------------------------------------------------------
Black, F., and M.S. Scholes (1973) "The Pricing of Options and Corporate Liabilities", Journal of Political Economy, 81 (May/June). 637-659
+----------+ ----+ Examples +---------------------------------------------------------
clear all
sysuse bsopm.dta, clear
db bsopm
bsopm ps pk , ir(0.12) time(0.50) sig(0.25)
bsopm ps pk , ir(ir) time(t) sig(sig)
. bsopm ps pk , ir(ir) time(t) sig(sig)
======================================================= * Black-Scholes European Pricing Option Model ======================================================= - Ps = Stock Pric = 100.0000 - PK = Strike Price = 110.0000 - Time = Expiration Time = 0.5000 - IR = Interest Rate = 0.1200 - Sig = Standard Deviation = Volatility = 0.2500 - CALL = Call Price = 5.5149 - Put = Put Price = 9.1090 =======================================================
+--------+ ----+ Author +-----------------------------------------------------------
Emad Abd Elmessih Shehata Assistant Professor Agricultural Research Center - Agricultural Economics Research Institute - Eg > ypt Email: emadstat@hotmail.com WebPage: http://emadstat.110mb.com/stata.htm WebPage at IDEAS: http://ideas.repec.org/f/psh494.html WebPage at EconPapers: http://econpapers.repec.org/RAS/psh494.htm
Sahra Khaleel A. Mickaiel Professor Cairo University - Faculty of Agriculture - Department of Economics - Egypt Email: sahra_atta@hotmail.com
+----------------+ ----+ bsopm Citation +---------------------------------------------------
Shehata, Emad Abd Elmessih & Sahra Khaleel A. Mickaiel (2012) BSOPM: "Stata Module to Compute Black-Scholes European Option Pricing Model"
Online Help:
bsopm, impvol. (if installed).