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).