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荔枝🐸 · 2025年07月05日

想请问一下计算AI0和AIt的100/2是什么呀

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.

想请问一下计算AI0和AIt为什么要乘100/2呀,这个代表什么呢?为啥不是55/180*3%*0.5(每半年付息一次)呢

1 个答案

李坏_品职助教 · 2025年07月05日

嗨,爱思考的PZer你好:


AI0 = [55/(55 + 125)] × 3% × 100/2 = 0.458


因为距离下一次支付利息还剩125天,而距离上一次支付利息已经过去55天,所以是55/(55 + 125)。 3%是票面利率。假如是1年支付一次利息的话,那么AI0 = 55/(55 + 125) * 3% * 100(100可以看做一份债券的面值),但现在是半年支付一次利息,所以最后再除以2.



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NO.PZ2025040202000067 问题如下 analyst gathers the following information about a bonfutures contraanthe unrlying semiannupbon If the quotefutures priis 138, baseon the carry arbitrage mol this futures contrais: A.A.unrvalue B.B.fairly value C.C.overvalue A Incorrebecause the quotefuturespriis greater ththe equilibrium futures price; hence, the futurescontrais overvaluerather thunrvaluebaseon its quoteprice.B Incorrebecause the quotefuturespriis greater ththe equilibrium futures price; hence, the futurescontrais overvaluerather thfairly valuebaseon its quoteprice.C Correbecause,accorng to the carry arbitrage mol, Q0 = [1/CF] {FV[+AI0] – AIT – FVCI}, where = Conversion factor, =Clebonprice, AI0 = Accrueinterest value te, AIT =Accrueinterest futures expiration, anFV= Future value of couponspaiAccrueinterest value te: AI0 =[55/(55 + 125)] × 3% × 100/2 = 0.458Accrueinterest futures expiration: AIT =[(30 + 55)/(55 + 125)] × 3% × 100/2 = 0.708FV[+ AI0] =(103 + 0.458) × (1 + 3.25%)30/360 = 103.734Substituting: Q0 = [1/0.75]{103.734 – 0.708 – 0} = 137.37The quotefutures priof 138 is greaterththe equilibrium futures priof 137.37; thus, the futures contraisovervalue 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bon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bon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

2025-05-11 16:05 1 · 回答