MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur télécharger pdf (Page 99)

Eighth Section

8. Case Studies

In the following sub-section, some very useful examples with functions and

scripts are illustrated. Read, implement and execute the codes that are

given. Try to change the code. Experiment by adding your own command

lines. Of course, for the needs of the course, you can find all needed

functions, scripts and datasets in the folder named as:

“Matlab Examples”

Depending on the place you are, this folder may be in different locations.

Send me an email or ask me in class for the exact location of this folder.

8.1 The Black – Scholes- Merton Options Pricing Formula

The Black Scholes Merton (BSM) model expresses the value of an option as a

function of the current value of a stock, S, the option’s strike price, X, the

option’s time to maturity, T, the volatility, s, of the stock price returns (this

is the standard deviation of the log-relative returns of the stock for the past

n days, where n is usually set equal to 60), the risk free rate, r, that prevails

for a maturity T and the stock’s dividend yield, d. The analytic formula for

the a European call option derived by BSM is:

)d(NXe)d(NSec

rTTdBSM

−−

−=

where,

?)/sdr()X/Sln(

+−+

= ,

Tsdd −=

and,

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MATLAB FINANCIAL DERIVATIVES TOOLBOX Manuel d'utilisateur Page 99