Problem 4. (10 Points) Consider a two-step binomial model with S(0) = 100 and returns on the stock u = 0.1 and d = 0.2. Let the risk-free return be r = 0 per step. Suppose that the stock pays a dividend of 10 at step 1 and a dividend of 5 at step 2.

(a) (2 Points) Draw the (ex-dividend) stock price tree.

(b) (2 Points) Calculate the risk-neutral probability p* at each node (0, 0), (1, 0), (1, 1).

(c) (2 Points) Compute the initial price CE(0) of a European call option with strike price X = 80 and expiration date N = 2.

(d) (2 Points) Compute the initial price PE(0) of a European put option with strike price X = 80 and expiration date N = 2. (e) (2 Point) Verify that the Put-Call Parity holds.