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)xtLet 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).