Each of the following problems worth 2 points. (a) (2 points) State the put-call parity. (b) (2 points) In the N-step binomial model, give an optimal stopping time for an Ameri- can option of payoff g (Si) = (S; - K)+ for each 0 s i s N on a stock with price (Si)osisN and a fixed constant K. (c) (2 points) Under the assumption of no arbitrage, can one always find a unique risk- neutral probability distribution? Give a brief justification or a counterexample. (d) (2 points) State the Black-Scholes equation for European option values. Give a brief description of how one might use it in practice. (e) (2 points) Suppose the stock price (St)ostsi during a period [0, 1] is given by St = So exp ((0.02) t + Bt), where (Boosts] is a Brownian motion. Compute the expected stock price at time 1