Returning the results of a function in a matrix

Hi there,

I am currently writing a program to predict default probabilities. My problem is that I need the function to be repeated for "i" times for each "T" and I would like to get the results of the simulation collected in a "i x T" matrix. So far I could not solve that problem and I would be happy if someone could give me a hint how to get a "NumberofDefault" matrix, that can be used for further analysis. I attached a sample, that is not meant to be financially correct, but hopefully illustrates what I did and what I need.

 % function [NumberofDefaults]=Diffusion(T)
%%Setting the Variables
n = T*100                    % 100 steps for each time period
M = 10000;                   % Number of Monte Carlo Steps
r = 0.05;                    % Riskless Interestrate
sigma = 0.1;                 % Volatility
phi = 0.02;                  % Change of the barrier
%%Creating the Random variable
x=randn(n,M)*sigma*T/n + (r-sigma/2-phi)*T/n; 
aux1= x;
X = randi([1001,2000],M,1)/1000;
X=log(X);
aux2=[X';aux1];
%%Matrix that is to be analysed
X=cumsum(aux2);
%%Returning all default events
out=arrayfun(@(n) min([ 0 X(find(X(:,M)<0,1),n)]),1:size(X,2));
out2=exp(out(out~=0));
NumberofDefaults = length(out2);             % Counting all columns with negative entries of X

Thank you very much in advance for any help and sorry for any effort. Thorsten Erdmann

Answer 1

[A Jenkins]

If your function above is working, you can just call it from another function as many times as you need. Of course if you are doing a large Monte Carlo this might get slow and you may need to find a way to optimize it.

function NumberofDefaultsMatrix=DiffusionMatrix(idx,T)
% call this with the desired number of iterations at each time period T

% this just initializes the matrix so your code runs faster
NumberofDefaultsMatrix=zeros(idx,T);

% construct the matrix
for tt=1:T  % for each time T
    for ii=1:idx  % run idx iterations
        NumberofDefaultsMatrix(ii,tt)=Diffusion(tt);
    end
end

end  % end DiffusionMatrix(idx,T)

% this is the function you already wrote
function NumberofDefaults=Diffusion(tt)
%rest of your code here...
%...
%...
end