Problem 1. An Exotic Binomial Model (9 pts) Consider a 2-period stock price model. Let r = 0.05 be the discrete interest rate for each of the periods, So = 100 and suppose that the stock price follows four possible scenarios: Syu Scenario Si S2 1- a* 103 Su suu 2 Si 103 100 W3 90 sau 1-7* sdu B* 90 80 90 1 B* 80 It is known that the risk-neutral probability for each scenario wi, i = 1, 2, 3, 4 satisty P* (wi) = = 0.2, P* (W2) = 0.4, P* (W3) = 0.3, P*(w4) = 0.1. (a) (2 pts) Find the risk-neutral probability a*, B*, and y* for each route on the tree. (b) (2 pts) Find the prices S, suu, and squ. (c) (2 pts) Find today's price of a European call option on this stock with strike price X = $100 maturing after two steps. (d) (3 pts) Find today's price of an American put option with strike price $110 and expiration date in two steps. Should the American option be exercised early? If so, when