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Aurora · 2025年05月11日

不太明白这里accrued interest的计算

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.

  1. 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
  2. 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

1 个答案

李坏_品职助教 · 2025年05月11日

嗨,努力学习的PZer你好:


这个不会重复计算。


AI指的是站在当前的这个时刻,从上一次支付利息到现在过去了多少天,这几天积累的利息。 只要债券的现货没有进行交易或交割,那么AI就会一直积累下去 直到下一次支付利息的时候再重新计算。




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虽然现在很辛苦,但努力过的感觉真的很好,加油!