1. Suppose it is known that the cheapest-to-deliver bond will be a 10% coupon bond with a conversion factor of 1.4623. Suppose also that the delivery will take place in 265 days (=0.7260 years). Coupons are payable semiannually on the bond. The last coupon was paid 40 days ago, the next coupon is due in 142 days (=0.3890 years), and the coupon date thereafter is in 325 days. The term structure is flat, and the rate of interest (with continuous compounding) is 8% per annum. Assume that the current quoted bond price is $120. Find the equilibrium cash futures price today using the parity condition.

2.

The spot exchange rate E = $0.95 US / FOREX. The U.S. interest rate is 3% per annum. The interest rate in the foreign country is 2% per annum. A futures contract for delivery of 1 million units of the foreign currency one year from today is trading now at F = $0.92 US / FOREX. Which of the following is true? An arbitrage strategy

1. Doesnt exist
2. Would involve buying the futures contract and borrowing in the foreign currency
3. Would involve selling the futures contract and borrowing in U.S. dollars.

Show your work to arrive at the choice above.

3. It is December now. A March futures contract on 10,000 MMBtu of natural gas settled for $4.95 per MMBtu. Assume that the contract has exactly 3 months (0.25 years) to maturity. The spot price is $4.78. Present value of three months worth of storage costs is $.05 per MMBtu. The interest rate is 3% annually. Assume convenience yield to be zero. Use continuous compounding.

1. Using the formula for commodity futures parity, F = {S + PV(c)}*e^rT, establish that an arbitrage opportunity exists.

2. Design the arbitrage strategy. Show profit for 10,000 MMBtu, i.e. per one futures contract