Monte Carlo Simulation in Matlab

I'll have to admit that I don't always use Excel for Monte Carlo simulation. If you don't have a Monte Carlo add-in for Excel, running a simulation with over 100000 points is not very practical. I usually use Matlab in that case (which is likely available somewhere on campus, if you are attending a university).

The trick to using Matlab for Monte Carlo simulation is to avoid using loops, since loops are particularly slow in Matlab. The example m-file below uses element-wise vector operations instead of loops. You don't need the Statistics Toolbox to use this code.

For more information about how Monte Carlo simulation works, please read "Monte Carlo Simulation in Excel: A Practical Guide".

% Example Monte Carlo Simulation in Matlab
% Function: y = x2^2/x1
%
%   Generate n samples from a normal distribution
%     r = ( randn(n,1) * sd ) + mu
%     mu : mean
%     sd : standard deviation
%
%   Generate n samples from a uniform distribution
%     r = a + rand(n,1) * (b-a)
%     a : minimum
%     b : maximum

n = 100000;	% The number of function evaluations

% --- Generate vectors of random inputs
% x1 ~ Normal distribution N(mean=100,sd=5)
% x2 ~ Uniform distribution U(a=5,b=15)

x1 = ( randn(n,1) * 5 ) + 100;
x2 = 5 + rand(n,1) * ( 15 - 5 );

% --- Run the simulation
% Note the use of element-wise operations

y = x2.^2 ./ x1;

% --- Create a histogram of the results (50 bins)

hist(y,50);

% --- Calculate summary statistics

y_mean = mean(y)
y_std = std(y)
y_median = median(y)

[ Monte Carlo Simulation ]