Question

It is March 10, 2017. The cheapest-to-deliver bond in a December 2017 Treasury bond futures contract is an 8% coupon bond, and delivery is expected to be made on December 31, 2017.

Coupon payments on the bond are made on March 1 and September 1 each year. The rate of interest with continuous compounding is 5% per annum for all maturities. The conversion factor for the bond is 1.2191. The current quoted bond price is $137. Calculate the quoted futures price for the contract.

Answer 1

Answer - Quoted price = 111.68

Explanation

The cash bond price is currently

137 + (9/184)*4 = 137.1957

A coupon of 4 will be collected after 175 days or we can say 0.4795 years. The present value of the coupon on bond is 4e^-0.05×0.4795 =3.9053 and the futures contract lasts 296 days or we can say 0.811 years.The cash futures price if it were written on the 8% bond would therefore be

= (137.1957 − 3.9053)e^0.05×0.8110

=138.8061

At delivery there would be 121 days of accrued interest and the quoted futures if the contract were written on the 8% bond would therefore be

138.8061 - (121/182)*4 = 136.1468

The quoted price should therefore be

= 136.1468/1.2191

Quoted price = 111.68