CODEWITHSUNDEEP
matlab
QFi
QFi

Reputation: 291

Avoiding for loops in Monte-Carlo simulation

I am running a Monte-Carlo simulation to calculate Y such as: Y(i,j+1)=Y(i,j)*a(i,j)+b

I would like to avoid when possible the use of for loop, and use instead matrix computation as it's the advantage of Matlab.

Here is my code: 

kappa = 6.21;
theta = 0.019;
sigma = 0.61;
rho = -0.7;
r = 0.0319;
V0 = 0.010201;
T = 1;
N = 300; % Time steps
M = 1e6; % Number of simulations

dt = T/N;
Z = randn(M,N);
a = kappa*dt+sigma*sqrt(dt);
b = kappa*theta*dt;

% With loop
tic
y = zeros(M,N); % preallocate
y(:,1) = V0; % initial value
for i=1:M
    for j = 1:N
        y(i,j+1) = y(i,j)*(1-a*Z(i,j))+b;
    end
end
toc

This is a small part of my entire code and alone it takes 65 seconds to run for the given parameters. Is there a way to make it faster, by doing matrix computation instead of loops? Thank you

Upvotes: 1

Views: 184

Answers (1)

Nakini
Nakini

Reputation: 772

Seems like, every column is dependent on the previous column values except the 1st column. So, you could get rid of the first for-loop by doing something similar to the following:

for j=2:N
    y(:,j) = y(:,j-1).*(1-a*Z(:,j-1)) + b;
end

This one reduces the time by almost half.

Upvotes: 2

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