bm.m

Brownian Motion, Option.

% This program simulates Brownian motion and Geometric Brownian motion. 

fprintf('\n This program simulates:')
fprintf('\n 1. Brownian motion \n 2. Geometric Brownian motion \n')
type = input('\n Choose one of the above options (enter 1 or 2): ');

mu = input('\n Enter parameter mu: '); 
sigma = input('\n Enter paremeter sigma: ');
S0 = input('\n Enter value at time 0: ');
T = input('\n Enter the time horizon T: ');
n = input('\n Enter the number of points in the discretization: ');

delta = T/n;
S = S0;
alpha = mu - sigma^2/2;

switch type 
    
    case 1 
        
        for i=1:n
            S = [S; S(i) + mu*delta + sigma*sqrt(delta)*randn];
        end
        plot(delta*[0:1:n], S,'b')
        title(['Brownian motion, \mu = ',num2str(mu),',\sigma = ',num2str(sigma)])
        xlabel('t')
        
    case 2
        
        for i=1:n
            S = [S; S(i)*exp(alpha*delta + sigma*sqrt(delta)*randn)];
        end
        plot(delta*[0:1:n], S, 'g')
        title(['Geometric Brownian motion, \mu = ',num2str(mu),',\sigma = ',num2str(sigma)])
        xlabel('t')
        
    otherwise
        
        fprintf('\n Error: That is not a valid option \n')
        
end