You are to price options on a futures contract. A binomial tree models the movements of the futures price. You are given the following information:
- Each period is 6 months, h=6months,
- Time to maturity of an option, T=1 year
- u/d=4/3, where u is 1 plus the rate of gain on the futures price if it is goes up, and
d is 1 plus the rate of loss if it goes down.
- The risk-neutral probability of an up move, p*=1/3.
- The initial futures price is $80.
- The continuously compounded risk-free interest rate is 5%.
- Let CE be the price of a 1-year 85-strike European Call option on the futures contract, and CA be the price of an otherwise identical American call option on futures contract.
Determine the difference between two prices; CA - CE