Given a risk-neutral stock price in the form of geometric brownian motion (GBM),
we will demonstrate the computation of the discretely monitored lookback put premium. Let the option maturity be , and the discretely monitored dates be . Then, the discretely monitored lookback put premium is given by the formula
We would compute option price computed by Page 70 of the paper [BGK99],
The exact answer should be according to the paper above.
Matlab code is here. 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.