Suppose it is known that the cheapest-to-deliver bond will be a 10% coupon bond
ID: 2817914 • Letter: S
Question
Suppose it is known that the cheapest-to-deliver bond will be a 10% coupon bond with a conversion factor of 1.4623. Suppose also that the delivery will take place in 265 days (=0.7260 years). Coupons are payable semiannually on the bond. The last coupon was paid 40 days ago, the next coupon is due in 142 days (=0.3890 years), and the coupon date thereafter is in 325 days. The term structure is flat, and the rate of interest (with continuous compounding) is 8% per annum. Assume that the current quoted bond price is $120. Find the equilibrium cash futures price today using the parity condition.
Explanation / Answer
Answer- The last coupon was paid 40 days ago, so duration from last coupon date to today is 40 days.
duration between last coupon date and next coupon date is 182 days (40 + 142).
The cash price of the bond is - 120 + (40/182)X 5 (a coupon of 10 received annually, so it is 5 for semiannually)
= 120 + 1.10 = 121.10
a coupon of 5 will be received in 142 days (=0.3890 years) time from now. The present value of the coupon is - 5e-0.3890 X 0.08 = 4.85
delivery will take place in 265 days, so future contract lasts for 265 days (=0.7260 years). The cash future price if the contract were written on 10% bond would be- (121.10 - 4.85)e0.7260X0.08 = 123.20.
Taking into consideration the conversion factor the cash future price should be- 123.20/1.4623 = 84.25.