6. In this problem we will use Monte Carlo to simulate the behavior of the martingale St/Pt , with Pt as numeraire. Let x0 = S0/P0(0, T ). Simulate the process xt+h

= (1+ σ

√

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

a. Evaluate P0E ST /PT (T , T) > K

.

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

− x0. Did you simulate a martingale?

c. Verify that the result is approximately the same as the price of a cash-ornothing call computed as e

−rT N(d2) ($0.5766 for the above parameters).