Thursday, February 18, 2010

Option Pricing Black-Scholes script for MATLAB and FreeMAT

function [C, P]= option_bs(S,X,r,sigma,days)
    %  This function to calculate Call and Put price per Black-Scholes formula.
    %  This function can be run both at FreeMAT and MATLAB,
    %  This function should be same as MATLAB's financial toolbox function
    %  blsprice.
    % C: call price
    % P: put price
    % S: stock price at time 0
    % X:  strike price
    % r: risk-free interest rate
    % sigma: volatility of the stock price measured as annual standard deviation
    % days: numbers of days remaining in the option contract, this will be converted into unit of years.
    % Black-Scholes formula:
    %  C = S N(d1) - Xe-rt N(d2)
    %  P = Xe-rt N(-d2) - S N(-d1)


    % for call
    d1 = (log(S/X) + (r + 0.5*sigma^2)*T)/(sigma*sqrt(T));
    d2 = d1 - sigma*sqrt(T);
    N1 = 0.5*(1+erf(d1/sqrt(2)));
    N2 = 0.5*(1+erf(d2/sqrt(2)));

    C = S*N1-X*exp(-r*T)*N2;

    % for put

    N1 = 0.5*(1+erf(-d1/sqrt(2)));
    N2 = 0.5*(1+erf(-d2/sqrt(2)));

    P = X*exp(-r*T)*N2 - S*N1;


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  3. If there is n=365 how the code is for each i? (i=1,2,3,...,365)

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