1. The May WTI futures price is $95.79/bbl. The annualized volatility (sigma) for June WTI futures is .1851. The continuously compounded, annualized risk free interest rate is .015.

a. Construct a binomial tree of possible futures values in 4 weeks assuming one week time intervals (i.e., delta t=1/52). (Hint: what is u? What is d?)

b. What is the value of p for this futures contract?

c. Determine the value of a European call option on June WTI that expires in 4 weeks that has a strike price of $95/bbl. What is the value of an American call option on this contract? What is the delta of the American call? How many June futures do I need to hold to hedge a long position in the call? Is my futures position for hedging long or short? How many contracts do I need to replicate a short position in the call? Is my futures position for replicating long or short?

d. Determine the value of a European put option on the June WTI that expires in 4 weeks that is struck at $95/bbl. What is the delta of the put? How many contracts do I need to hold to hedge a long position in the put? Is my hedging position long or short? How many contracts do I need to hold to replicate a long position in the put? Is my replicating position long or short?

e. Determine the value of an American put option on June WTI futures that expires in 4 weeks that is struck at $110.00. Identify when the option will be exercised early (i.e., the nodes in the binomial tree where early exercise is optimal).