# Simulated Random Walk in MATLAB

0

Put in simple terms, a Random Walk basically involves taking successive random steps and tracing the trajectory. I adapted the example from part one of Wilmott on Quantitative Finance and wrote a quick MATLAB script to simulate a simple random walk. Basically flip a coin if it is heads multiply the equity seed by 1.01 and if its tails multiply by 0.99.

### Results

The graphs below show succesive runs of the script. I simulated 10,000 coin tosses in each test.

Sim one: You flipped 5069 heads & 4931 tails

Sim Two: You flipped 4946 heads & 5054 tails

Sim Three: You flipped 5026 heads & 4974 tails

Sim Four: You flipped 5042 heads & 4958 tails

### MATLAB Code

Writing the code in MATLAB is very straightforward I wrote the code in less then five minutes so it is a bit rough around the edges. I probably could refactor it but it does the job.

% Simple Simulated Random Walk Adapted
% from part 1 Paul Wilmott on Quant Fin

% create matrix with random int either 1 or 2
randMat = randi(2,10000,1);
randEquity = [1:10000];

tailCount = 0;
equitySeed = 100.00;

for i=1:10000
if randMat(i)==1
equitySeed = 1.01 * equitySeed;
randEquity(i) = equitySeed;
else
% must have flipped tails
tailCount = tailCount + 1;
equitySeed = 0.99 * equitySeed;
randEquity(i) = equitySeed;
end
end

plot(randEquity);
title('\bf \fontname{Arial} \fontsize{16}Simulated Random Walk');
xlabel('\bf \fontname{Arial} \fontsize{12}Number of Coin Tosses');
ylabel('\bf \fontname{Arial} \fontsize{12}Price in (\$)');

% clean-up
clear equitySeed headCount tailCount randMat i;