Please include all work, steps, and reasoning, including formulas used. Thank you so much!

Problem 6. Consider a two-step stock price model. Let r-0.05 be the risk-free return per period S(0) 100 and suppose that the stock price follows four possible scenarios Scenario S(1) S(2) 103 u1 100 Su 103 90Sdiu 9080 W2 du u3 W4 90 80 It is known that the risk-neutral probability for each scenario wi, i - 1,2,3,4 satisty P(0.2, P(0.4, P(w)-0.3, P(w0.1. (a) (2 points) Find the risk-neutral probability *, , and * for each route on the tree. (b) (2 points) Find the prices Su, Suu, and Sdu. (c) (3 points) Find today's price of an European call option on this stock with strike price X - $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 6. Consider a two-step stock price model. Let r-0.05 be the risk-free return per period S(0) 100 and suppose that the stock price follows four possible scenarios Scenario S(1) S(2) 103 u1 100 Su 103 90Sdiu 9080 W2 du u3 W4 90 80 It is known that the risk-neutral probability for each scenario wi, i - 1,2,3,4 satisty P(0.2, P(0.4, P(w)-0.3, P(w0.1. (a) (2 points) Find the risk-neutral probability *, , and * for each route on the tree. (b) (2 points) Find the prices Su, Suu, and Sdu. (c) (3 points) Find today's price of an European call option on this stock with strike price X - $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