4. Treasury Futures (Medium-Hard, 25 points) This problem guides you through how to price a Treasury futures contract. You have already learned the two pieces: how the last set- tlement price is converted to the cash paid for the actual bond that is delivered, and how to calculate forward/futures prices. You now need to combine these. You want to price a one-year Treasury bond futures contract. Suppose you know that the cheapest to deliver bond will (for sure) be the bond that currently has 17 years and 4 months to maturity, and a coupon rate of 3% with coupons paid out semiannually. Suppose that all zero rates up to one year of maturity are 2.0% per year with continuous compounding. (a) (10 points) Compute the conversion factor for the bond at the delivery date. Hint: if the bond currently has 17 years and 4 months, how long will it have left when delivered? the bond (b) (3 points) What is the net present value of the two coupon payments made over the lifetime of the futures contract? (c) (5 points) Suppose the dirty" price of the bond today is $98 per $100 of face value. (This is the actual amount of money you have to pay to get the bond. Bonds are usually quoted as clean prices, with the "dirty" price being the clean price plus accrued interest.) What would be the price on a one year forward contract on this bond? (d) (7 points) What is the Treasury bond futures price? You may ignore the difference between futures and forward prices. Hint: start with your answer to part (c). Recall that in the futures contract, the party with the short position receives futures price x conversion factor + accrued interest for the bond. In (c) you figured out a forward price: the amount of cash that should be promised in return for the bond. What Treasury futures price will give you this same pay- ment? 4. Treasury Futures (Medium-Hard, 25 points) This problem guides you through how to price a Treasury futures contract. You have already learned the two pieces: how the last set- tlement price is converted to the cash paid for the actual bond that is delivered, and how to calculate forward/futures prices. You now need to combine these. You want to price a one-year Treasury bond futures contract. Suppose you know that the cheapest to deliver bond will (for sure) be the bond that currently has 17 years and 4 months to maturity, and a coupon rate of 3% with coupons paid out semiannually. Suppose that all zero rates up to one year of maturity are 2.0% per year with continuous compounding. (a) (10 points) Compute the conversion factor for the bond at the delivery date. Hint: if the bond currently has 17 years and 4 months, how long will it have left when delivered? the bond (b) (3 points) What is the net present value of the two coupon payments made over the lifetime of the futures contract? (c) (5 points) Suppose the dirty" price of the bond today is $98 per $100 of face value. (This is the actual amount of money you have to pay to get the bond. Bonds are usually quoted as clean prices, with the "dirty" price being the clean price plus accrued interest.) What would be the price on a one year forward contract on this bond? (d) (7 points) What is the Treasury bond futures price? You may ignore the difference between futures and forward prices. Hint: start with your answer to part (c). Recall that in the futures contract, the party with the short position receives futures price x conversion factor + accrued interest for the bond. In (c) you figured out a forward price: the amount of cash that should be promised in return for the bond. What Treasury futures price will give you this same pay- ment
