# Question

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).

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).

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