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

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.Note that option matures after 10 periods. Please explain by building a futures price tree.

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. Please explain by building a tree of chooser option payoffs (and not using any formulas that I have seen this question answered before)