1. a. Background: You should build a 15-period binomial model whose parameters are calibrated to a Black-Scholes geometric Brownian motion model with: T = 0.25 years, S₀ = 100, r = 2%, = 30% and a dividend yield of c = 1%. Your binomial model should use a value of u = 1.0395 ... (This has been rounded to four decimal places but you should not do any rounding in your spreadsheet calculations.) compute the price of an American call option with strike K = 110 and maturity T = .25 years. Round all your answers to 2 decimal places.

b. Following the background in Question 1a. Compute the price of an American put option with strike K = 110 and maturity T = .25years. Round all your answers to 2 decimal places.

c. Following the background in Question 1a. Is it ever optimal to early exercise the put option of Question 1b? Round all your answers to 2 decimal places.

d. Following the background in Question 1. If the answer to Question 1c is "Yes". when is the earliest period at which it might be optimal to early exercise? (If your answer to Question 1c is "No then you should submit an answer of 15 since exercising after 15 periods is not an early exercise.) Round all your answers to 2 decimal places.

e. Following the background in Question 1a. Do the call and put option prices of Questions 1a and b satisfy put-call parity? Round all your answers to 2 decimal places.

f. Following the background in Question 1. 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 contracts on the same underlying security of the previous questions. Round all your answers to 2 decimal places.

g. Following the background in Question 1. What is the earliest time period in which you might want to exercise the American futures option of Question 1f? Round all your answers to 2 decimal places.