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%, σ=30% and a dividend yield of c=1%. Your binomial model should use a value of u=1.0395....

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=110 and maturity T=.25 years.

3. Is it ever optimal to early exercise the put option of Question 2?

4. 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.

5. 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 = 100K and they mature 5 periods later, i.e. at n = 15