NO.PZ2025040202000067
问题如下:
An analyst gathers the following information about a bond futures contract and the underlying semiannual pay bond:
If the quoted futures price is 138, based on the carry arbitrage model this futures contract is:
选项:
A.A.undervalued. B.B.fairly valued. C.C.overvalued.解释:
A Incorrect because the quoted futures
price is greater than the equilibrium futures price; hence, the futures
contract is overvalued rather than undervalued based on its quoted price.
B Incorrect because the quoted futures
price is greater than the equilibrium futures price; hence, the futures
contract is overvalued rather than fairly valued based on its quoted price.
C Correct because,
according to the carry arbitrage model, Q0 = [1/CF] {FV[B0 +
AI0] – AIT – FVCI}, where CF = Conversion factor, B0 =
Clean bond price, AI0 = Accrued interest at value date, AIT =
Accrued interest at futures expiration, and FVCI = Future value of coupons
paid.
Accrued interest at value date: AI0 =
[55/(55 + 125)] × 3% × 100/2 = 0.458
Accrued interest at futures expiration: AIT =
[(30 + 55)/(55 + 125)] × 3% × 100/2 = 0.708
FV[B0 + AI0] =
(103 + 0.458) × (1 + 3.25%)30/360 = 103.734
Substituting: Q0 = [1/0.75]
{103.734 – 0.708 – 0} = 137.37
The quoted futures price of 138 is greater
than the equilibrium futures price of 137.37; thus, the futures contract is
overvalued.
- AI0是因为在现在的时间点,距离上一次支付coupon过去了55天,所以是在这55天里面产生的interest
- AI(T)是,在我持有这个bond的期间,直到下一次coupon的时间,在这段我持有的时间内累计的interest还是属于我(虽然这笔coupon我拿不到)。答案里面用了30+55,我明白这是在上一次coupon之后,到交割,这个bond属于我的时长,但是在计算AI0的时候也考虑了这55天,这样不会导致重复计算吗?
谢谢