Explanation:
First, calculate the cash price for the CTD bond as the quoted bond price plus accrued interest (AI). Note that since it is April 1, there have been 90 days since the last coupon.
AI = 2 × (90/180) = 1.0. Cash price = 98 + 1.0 = 99.
Next, since the next coupon will be received on July 1 (90 days from today), that cash flow should be discounted back to the present:
2e^(-0.02(90/365)) = $1.99
Using the cost of carry model, the cash futures price of the contract expiring 180 days from today is calculated as:
F₀ = (99 − 1.99)e^(0.02)(180/365) = $97.97
Here is the tricky part: the futures contract expires 90 days after the July 1 coupon payment, so the accrued interest must be subtracted:
$97.97 − [2 × (90/180)] = $96.97
Finally, the conversion factor is applied, producing a theoretical price for the T-bond futures contract of:
QFP = $96.97 / 1.12 = $86.58
(Book 3, Module 45.2, LO 45.g)
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Question 65
The cheapest-to-deliver (CTD) bond for a Treasury bond futures contract pays 4.0% semiannual coupons on January 1 and July 1. This CTD bond has a conversion factor of 1.12 and a quoted bond price of 98. Assume it is now April 1, 2025, and that the Treasury bond futures contract is to be delivered 180 days from today. The current risk-free interest rate is 2.0%. What is the theoretical price for this T-bond futures contract?
A
$86.58.
B
$87.50.
C
$96.97.
D
$97.97.
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