Question

It's July 30, 2017. The cheapest-to-deliver bond in a Sept 2017 Treasury bond futures contract is a 9% coupon bond and delivery is expected to be made on Sept 30, 2017. Coupon payments on the bond are made on Feb 4 and Aug 4 each year. The term structure is flat, and the rate of interest with continuous compounding is 9% per annum. The conversion factor of the bond is 1.7. The current quoted bond price is $107. Calculate the quoted futures price of the contract.

(required precision: 0.01 +/- 0.01)

Answer 1

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Answer:

There are 176 days between February 4 and July 30 and 181 days between February 4 and August 4. The cash price of the bond is, therefore: 107 + 176/181 X 4.5 = 111.3756 The rate of interest with continuous compounding is 21n1.045 =or 8.80% per annum A coupon of 4.5 will be received in 5 days (= 0.01370 years) time. The present value of the coupon is 4.5e^-0.01370*0.088 = 4.49 The futures contract lasts for 62 days (= 0.1699 years). The cash futures price if the contract were written on the 9% bond would be (111.3756 - 4.49) e^0.1699*0.088 = 108.496 At delivery there are 57 days of accrued interest. The quoted futures price if the contract were written on the 9% bond would therefore be 108.496-4.5 X 57/184 = 107.10 Taking the conversion factor into account the quoted futures price should be: 107.10/1.7 = 63.00