# Monte Carlo Simulation in Matlab

**Supplement to**"A Practical Guide to Monte Carlo Simulation",

*by Jon Wittwer, PhD*

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)

### REFERENCES:

- Huber, T., "Introduction to Monte Carlo Simulation",
*http://physics.gac.edu/~huber/envision/instruct/montecar.htm* *The Matlab Central File Exchange*, Statistics and Probability,*http://www.mathworks.com/matlabcentral/*