Given a risk-neutral stock price in the form of geometric brownian motion (GBM),
we will demonstrate the computation of the call premium. Let the option maturity be and strike Then, the discretely monitored lookback put premium is given by the formula
Matlab code is here. Let
The exact answer should be according to the BS formula.
The method is simple:
step1. Use the standard Euler method with intervals in to simulate the path of , compute discounted payoff of the sample path;
step 2. Repeat the path simulation of step 1 times, and take the average.
The result shows that if and , then the option price is with confidence interval . The total running time on my desktop PC is seconds.