7. We now use Monte Carlo to simulate the behavior of the martingale Pt/St , with St as numeraire. Let x0 = P0(0, T )/S0. Simulate the process xt+h

= (1+ σ

√

hZt+h)xt Let h be approximately 1 day.

a. Evaluate S0E PT (T , T )/ST < 1/K

.

b. Compute the mean and standard deviation of the difference xT

− x0. Verify that you have simulated a martingale.

c. Verify that the result is approximately the same as the price of an asset-ornothing call computed as S0N(d1) ($26.4617 for the above parameters).