Build a 15-period binomial model with the following parameters: u = 1.0395, d = 1/u, S0 = 100 and the gross risk-free rate per period is R = 1.000333. (This risk-free rate per period corresponds to an annualized continuously-compounded risk-free rate of 2% and a period length of .01667 years. The total maturity is then 15 .01667 = 0.25 corresponding to an option maturity of 3 months.) Now answer the following questions: (a) Compute the price of an American call option with strike K = 110 and maturity T = .25 years. (5 marks) (b) Compute the price of an American put option with strike K = 110 and maturity T = .25 years. (5 marks) (c) Is it ever optimal to early exercise the put option of part (b)? (5 marks) (d) If your answer to part (c) is "Yes", when is the earliest period at which it might be optimal to early exercise? (5 marks) (e) Do the call and put option prices of parts (a) and (b) satisfy put-call parity? Why or why not? (5 marks)