You want to speculate on oil futures. You see that the current price of oil is $72 per barrel. You can borrow at 3% and lend at 2% (annual rates, continuously compounded). You want to enter into a forward contract for delivery of oil in 9 months. You are betting that the price of oil will fall, but before you can enter any contract, you need to determine what forward prices are appropriate. You also realize that the cost of storing oil is about 1% of the value of the oil itself, compounded continuously. Also, the convenience yield is about 2% of the value of the oil, compounded continuously. You don’t expect any other cash flows from investing in oil during the coming 9 months.

a. Determine the range of forward prices that this contract can take.

b. Your financial institution offers you a forward contract with a forward price of $79 per barrel for delivery in 9 months. Is there an arbitrage opportunity? If so, describe how to take advantage of it and show the resulting profits. If not, explain why this does not present an arbitrage opportunity. Assume no credit risk.