1. The June WTI futures price is $80.18/bbl. The annualized volatility (sigma) for June WTI futures is 36.71 percent. The continuously compounded, annualized risk free interest rate is .04

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 $78/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 $82/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 $82.00. Identify when the option will be exercised early (i.e., the nodes in the binomial tree where early exercise is optimal).

f. Value an American put on June WTI futures that expires in 4 weeks that is struck at $82, but now assume the interest rate is 30 percent and the volatility is 15 percent. Identify when early exercise is optimal.