Need solution methods and answers for 4,5,6 and 8. Thanks.

Questions 1-8 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%, =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.)

1. Compute the price of an American call option with strike K=110 and maturity T=.25 years.

2. Compute the price of an American put option with strike K=110and maturity T=.25 years.

3.Is it ever optimal to early exercise the put option of Question 2? YES or NO.

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? YES or NO.

6.Compute the fair value of an American call option with strike k=100 and maturity periods n=10where 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.

8.Compute the fair value of a chooser option 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.