Consider a 2-period binomial non-recombining model. Let r = 0.05 be the discrete interest rate for each of the periods, S(0) = 100 and suppose that the stock price follow four possible scenarios:

Scenario	S(1)	S(2)
?1	Su	Suu
?2	Su	103
?3	90	Sdu
?4	90	80

It is known that the risk-neutral probability for each scenario ?i , i = 1, 2, 3, 4 satisty P ? (?1) = 0.2, P? (?2) = 0.4, P? (?3) = 0.3, P? (?4) = 0.1.

(a) Draw the tree of the stock prices using S^u , S^uu, and S^du, and find the risk-neutral probability for each route on the tree.

(b) Find the prices S^u , S^uu, and S^du

(c) Find todays price of a European call option with strike price K = $100 maturing after two steps.

(d) Find todays 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?