# Simulated Random Walk in MATLAB

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 successive runs of the script. I simulated 10,000 coin tosses in each test.

Simulated Random Walk – Sim One: You flipped 5000 heads & 5000 tails

Simulated Random Walk – Sim Two: You flipped 5077 heads & 4923 tails

Simulated Random Walk – Sim Three: You flipped 4890 heads & 5110 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
clear equitySeed headCount tailCount randMat i;