% generate random paths and evaluate path-dependent options
M = 1e4; % # repeats
N = 1e2; % # time-steps
Z = randn(N,M);

r = 0.01; T = 1; sigma = 0.5; S0 = 1;

dt = T/N;

% create log returns
X = (r-sigma.^2/2)*dt + sqrt(dt)*sigma*Z;
% create log paths
X = cumsum(X); % cumulative sum of returns
% add initial values
X = [zeros(1,M); X];
% create asset values
S = exp(X);

% option payoffs (cashflows)

% example: option on the maximum value reached, strike 1
cashflows = exp(r*T)*max(max(S)-1,0);

% example: option on the average value, strike 1
cashflows = exp(r*T)*max(mean(S)-1,0);

% example: barrier option, European payoff, but zero payoff if the asset reaches 2
cashflows = exp(r*T)*max(S(end,:)-1,0).*(max(S)<2);

V = mean(cashflows), e = std(cashflows)*1.96/sqrt(M)