MATLAB FINANCIAL DERIVATIVES TOOLBOX Manual do Utilizador descarregar pdf (Página 100)

dze

)z(N

∫

∞−

−

represents the cumulative normal distribution function with mean zero and

unity standard deviation (the Matlab build in function is named as:

f).

The value of a European put option can also be defined via the BSM as:

)d(NSe)d(NXep

TdrTBSM

2 −−−=

−−

8.1.1 Implementation of the BSM Formula

We want to create a script named as OptionsBSM.m that calls the user

created function

e to price European call, c, and European put, p,

options using the Black, Scholes and Merton model (BSM). The function

e should take seven (at least six) input parameters (as single values

or in the form of a vector) and should return the value (or the vector) of a

European call or put. Its calling syntax should look like:

“[Price] =

e(S, X, T, vol, r, Index, dv)”

“Index” is a string input argument that is set as an additional input

argument that takes the values: 'CALL' (or any other spelling of the 'CALL'

such as 'Call', 'CaLL', etc), or 'PUT' (or any other spelling of the 'PUT' such as

'Put', 'PuT', etc) and should be used to define the kind of option type (use the

build in function

r to convert the “Index” to lower case). Note the “Index”

precedes “dv” because “dv” should be an optional input (will come back to

this in a while).

To validate the formula, via the script create a table that tabulates the call

and put values against the moneyness ratio, S, and maturity, T. The data

should be loaded from a text file (that the user creates either by hand or via

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