Problem 3. Recall the European call option example from the lecture. Let {Bt}t0 be Brownian motion. Let Xt=X0exp(t+Bt) denote the stock price at time t, and let Dt=ertXt be the discounted stock price. (a) [10] Show that if =r22, then {Dt} is a martingale. [Hint: Problem 2 may be helpful.] (b) [20] Show that if =r22, then E[erSmax(0,XSK)]=X0(S(r+22)Slog(K/X0))erSK(S(r22)Slog(K/X0)), where () is the cdf of a standard Normal distribution. Make sure to clearly explain each step of the derivation. [Hint: Write the expectation as an integral with respect to the density function for BS. Then, break up the integral into the part where XSK0 and the part where XsK