# Pricing options using a binomial tree

The past few months, I have been taking the financial engineering course offered by Columbia. It is a great course but there is a huge disconnect between the theory they teach and the questions then asked in their quizzes.

I have been stuck on the following problems for over a week now and would appreciate any hints or links to resources that explain the theory (it in not at all covered in the material they provide).

Context: We are meant to build a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with the following features: T=.25 years, S0=100, r=2%, σ=30% and a dividend yield of c=1%.

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 contract is on the same underlying security of the previous questions.

2. 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.

Thanks!