Problem 2. (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) (3 Points) Compute the initial price CE(0) of a European call option with strike price X = 80 and expiration date N = 2. (c) (3 Points) Compute the initial price PE(0) of a European put option with strike price X = 80 and expiration date N = 2. (d) (2 Point) Verify that the Put-Call Parity holds. Problem 2. (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) (3 Points) Compute the initial price CE(0) of a European call option with strike price X = 80 and expiration date N = 2. (c) (3 Points) Compute the initial price PE(0) of a European put option with strike price X = 80 and expiration date N = 2. (d) (2 Point) Verify that the Put-Call Parity holds