Assignment:
Each of the following questions should be answered by building a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with: T=.25 years,S0=100,r=2%,s=30% and a dividend yield of c=1%. Hint: 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.)
Question 1
Compute the price of an American call option with strike K=110 and maturity T= .25years.
Question 2
Compute the price of an American put option with strike K=110 and maturity T= .25years.
Question 3
Is it ever optimal to early exercise the put option of Question 2?
Question 4
If your answer to Question 3 is "Yes", when is the earliest period at which itmightbe 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.)
Question 5
Do the call and put option prices of Questions 1 and 2 satisfy put-call parity?
Question 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.
Question 7
What is the earliest time period in which you might want to exercise the American futures option of Question 6?
Question 8
Compute the fair value of achooseroption which expires after n=10 periods. At expiration the owner of the chooser gets to choose (at no cost) a European call option or a European put option. The call and put each have strike K=100 and they mature 5 periods later, i.e. at n=15.