Brownian Path Simulation - Plotting more than one path

Question

0 个投票

I am to create a discrete sample Brownian path. I believe I have the code complete, but if any mistakes, please do not hesitate in letting me know. I am trying to figure out how to generate 100, 1000, 10000 paths with T = 1 and n = 200. I'm not sure where exactly that goes. Thank you.

function [W] = brownianPath (T,n)
 %t = 0, T/n, 2T/n, ..., T where T = termination time & n = steps% 
 stepsize = T/n;
 t = 0:stepsize:T;
 dW = zeros(1,n);
 W = zeros(1,n);
 dW(1) = randn/sqrt(stepsize);
 W(1) = dW(1); %W(0) = 0 with probability 1%
 for m = 2:n
    dW(m) = randn/sqrt(stepsize);
    W(m) = W(m-1) + dW(m);
 end
 plot([0:stepsize:T],[0 W], 'g-');
 xlabel('t')
 ylabel('W(t)')
 end