Consider a Gap Put (see Section 14.5 in text) that pays

f(S_T) = (105 ST) if ST < 102; 0 otherwise . Assume S0 = 100, = 0.15, r = 0.06, = 0.03 and T = 1. We use a Black-Scholes model, so that S_T is log-normal.

Compute the risk-neutral probability Q(S_T< 102)

Compute the expected stock price (under Q) conditional on S_T< 102, ie E^Q[S_T |S_T < 102]

Using a Monte Carlo simulation with at least 100 simulations of S_T, find the approximate price this Gap Put today. Compare to the exact answer given by the formula (14.15) in textbook. [(14.15) gives the formula for Gap Call, but based on it and parts a/b, you should be able to derive the Gap Put]