Assume that today is October 15th. It is known that a certainTreasury bond is the...

Assume that today is October 15th. It is known that a certain Treasury bond is the cheapest to deliver bond on the Treasury futures contract. The cheapest to deliver bond has a 5% coupon and the last coupon payment was on June 3rd. Today’s quoted price for the bond is $92. The first day that delivery can take place is December 20th. Assume that the term structure of interest rates is constant and the rate of interest (based on continuous compounding) is equal to 6%. If the conversion factor for the cheapest to deliver bond is 0.8, what is the Treasury futures price?

Expert Solution

Current bond price	92+((134/365) x 5) =	$ 93.835
coupan of 5 will be received after 190 days or 0.5205 years
The present value of the coupan on the bond =	5e^(-.06x0.5205) =	$ 4.85
Time till the contract last is 66 days or 0.1808 years
The future value of the 5% bond is	(93.835 - 4.85) e ^ 0.06 x 0.1808 =	$ 89.955
Conversion Factor	0.8
Therefore quoted price	$ 89.955*0.8	$ 71.964

jeff jeffy answered 2 years ago

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