Please show all work/steps. Please do not use excel or other programs. Thanks

Problem 2. Consider a 2-period stock price model. Let r0.05 be the discrete interest rate for each of the periods, S(0) 100 and suppose that the stock price follows four possible scenarios Su Scenario S(1) S(2) Su Suu Su 103 90Sdu 90 80 103 100 u2 du u3 90 80 It is known that the risk-neutral probability for each scenariowi,i-1,2,3, 4 satisty (a) (3 points) Find the risk-neutral probability *, , and * for each route on the tree (b) (3 points) Find the prices S", Su, and Sdu (c) (3 points) Find today's price of a European call option on this stock with strike price = $100 maturing after two steps (d) (5 points) 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? Problem 2. Consider a 2-period stock price model. Let r0.05 be the discrete interest rate for each of the periods, S(0) 100 and suppose that the stock price follows four possible scenarios Su Scenario S(1) S(2) Su Suu Su 103 90Sdu 90 80 103 100 u2 du u3 90 80 It is known that the risk-neutral probability for each scenariowi,i-1,2,3, 4 satisty (a) (3 points) Find the risk-neutral probability *, , and * for each route on the tree (b) (3 points) Find the prices S", Su, and Sdu (c) (3 points) Find today's price of a European call option on this stock with strike price = $100 maturing after two steps (d) (5 points) 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