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 S0EPT (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-or nothing call computed as S0N(d1) ($26.4617 for the above parameters).