Interest Rate Futures Chapter 6 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

Day Count Conventions in the U.S. Treasury Bonds: Actual/Actual (in period) Corporate Bonds: 30/360 Money Market Instruments: Actual/360 Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

Example 1. Actual/actual Bond principal is $100, coupon payment dates are March 1 and Sep 1. Coupon rate is 8% per annum. Suppose that we wish to calculate interest between March 1 and July 3. $4 coupon payments on Mar 1 and Sep 1 Reference period is Mar 1-Sep 1: 184 actual days Nr. of days btw dates: Mar 1-July 1: 124 actual days (124/184) x $4= 2.6957

2. 30/360 We assume 30 days in a month and 360 days in a year. Mar 1-Sep 1: 180 (6x30) days Mar 1-July 3: (4x30)+2=122 days (122/180)x4= 2.7111

Treasury Bond Price Quotes in the U.S Cash price = Quoted price + Accrued Interest Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

Example It is March 5, 2010, bond under the consideration is an 11% coupon bond matring on July 10, 2018 with a quoted price of 95-16 ($95.5). Coupons are paid semiannually on government bonds recent coupon date is Jan 10, 2010, next coupon date is July 10, 2010 Jan 10, 2010-Mar 5, 2010: 54 days Jan 10, 2010-July 10, 2010: 181 days (54/181)x $5.5 = $1.64 Cash price = 95.5+1.64= $97.14

Treasury Bond Futures Cash price received by party with short position = Most recent settlement price × Conversion factor + Accrued interest Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

Example Most recent settlement price = 90.00 Conversion factor of bond delivered = 1.3800 Accrued interest on bond =3.00 Price received for bond is 1.3800×90.00+3.00 = $127.20 per $100 of principal A party with short position in one contract would deliver bonds with face value of $100 and receive $127.2. Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

Conversion Factor The conversion factor for a bond is approximately equal to the value of the bond on the assumption that the yield curve is flat at 6% with semiannual compounding Options, Futures, and Other Derivatives, 7th International Edition, Copyright © John C. Hull 2008

Example 10% coupon bond with 20 years and two months to maturity: We assume that 20 years to maturity. Conversion factor= 146.23/100=1.4623

Cheapest to Deliver Bond It is the bond where; quoted bond price - (Most recent settlement price x conversion factor) is the least.

Example 6.1 The party with the short position has desided to deliver and is trying to choose btw the following three bonds. Assume that the most recent settlement price is 93-03, or 93.25. Find the cheapest to deliver bond. Bond Quoted bond price ($) Conversion Factor 1 99.50 1.0382 2 143.50 1.5188 3 119.75 1.2615

Determining the futures price If we assume that both the cheapest-to-deliver bond and the delivery date are known, the T-bond futures contract is a futures contract on a traded security (the bond) that provides the holder with known income.

Example 6.2 Suppose that in a T-bond futures contract, it is known that the cheapest-to-deliver bond will be a 12% coupon bond with a conversion factor of 1.6000. Suppose also that it is known that delivey will take place in 270 days. Coupons are payable semiannually on the bond. The last coupon date was 60 days ago, the next coupon date is in 122 days, and the coupon date thereafter is in 305 days. The term structure is flat, and the rate of interest (with cont. Compounding) is 10% per annum. Assume that the current quoted bond price is $115.