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.

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