Each of the following questions should be answered by building a 15-period binomial model whose parameters have been calibrated to a Black-Scholes geometric Brownian motion model with: T = 0.25 years,S0=100,r=2%,s=30%andadividendyieldofc=1%.

Your binomial model, as a result of the calibration, should use a value of u = 1.03949, d = 1/u, q = 49.247%. and R = exp(r*T/15) so that 1/R = exp(-r*T/15).

1. Compute the price of an American call option with strike K = 110 and maturity T = :25 years. 2. (5 pts) Compute the price of an American put option with strike K = 110 and maturity T = :25 years. 3. (5 pts) Is it ever optimal to early exercise the put option of Question 2?

4. If your answer to Question 3 is "Yes", when is the earliest period at which it might be optimal to early exercise? (If your answer to Question 3 is "No", then you should submit an answer of 15 since exercising after 15 periods is not an early exercise.)

5. Do the call and put option prices of Questions 1 and 2 satisfy put-call parity?

6. Compute the fair value of an American call option with strike K = 110 and maturity n = 10 periods where the option is written on a futures contract that expires after 15 periods. The futures contract is on the same underlying security of the previous questions.

7. What is the earliest time period in which you might want to exercise the American futures option of Question 6?