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];

headCount = 0;
tailCount = 0;
equitySeed = 100.00;

for i=1:10000
    if randMat(i)==1
        % we flipped a heads
        headCount = headCount + 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

fprintf('You flipped %i heads & %i tails\n', headCount, tailCount);
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;