Fix matlab code with error

Question

I understand that there is an error with dimensions in line dr=(r-v*v/2)*dT . But I have little knowledge of Matlab. Help to fix it, please. The code is small and simple. Maybe someone will find time to look

 function [optionPrice] = upAndOutCallOption(S,r,v,x,b,T,dT)
    t = 0;
    dr=[];
    pert=[];
    while (t < T) & (S < b)
        t = t + dT;
        dr = (r - v.*v./2).*dT;
        pert = v.*sqrt( dT ).*randn();
        S = S.*exp(dr + pert);
    end
    if S<b
        % Within barrier, so price as for a European option.
        optionPrice = exp(-r.*T).* max(0, S - x);
    else
        % Hit the barrier, so the option is withdrawn.
        optionPrice = 0;
    end
    end

Call from another function of this kind: for k=1:amountOfOptions [optionPrices(k)] = upAndOutCallOption(stockPrice(k)*o,riskFreeRate(k)*o,... volatility(k)*o, strike(k)*o, barrier(k)*o, timeToExpiry(k)*o, sampleRate(k)*o); result(k) = mean(optionPrices(k)); end

Therefore, any difficulties.

Answer 1

It's good that you know the problem is within dr = (r - v.*v./2).*dT;. The command itself has many possible problems which also related to dimensions:

1. Here you are doing element-wise multiplication (because of the .*) with matrices, which requires (in the case of your command) that r has the same number of rows AND columns as v (since because of element-wise, v.*v/2 has the same size as v).

2. Moreover, it is unnecessary to do element-wise division with scalar number, that means there is no need to have ./2 in Matlab.

3. And, finally, since it's element-wise multiplication again, the matrix (r - v.*v./2) must also have the same number of rows and columns as matrix dT.

Check here for more information about Matlab's matrix operations.