关于ai0和ait

NO.PZ2019010402000057

问题如下：

Aries is going to purchase a two-year Treasury note futures contract, The underlying 1.2%, semi-annual two-year Treasury note is quoted at a clean price of 103. It has been 60 days since the last coupon payment. Aries wants to calculate the full spot price of the underlying two-year Treasury note:

选项：

103.60

103.20

102.80

解释：

B is correct

本题考察的是计算一个两年期国库券的价格。

S₀ = Quoted bond price + Accrued interest = B₀ + AI₀

Accrued interest ( AI )= Accrural period × Periodic coupon amount = （NAD/NTD）× （C/n）

AI = (60/180) × (0.012*100/2) = 0.20.

S₀ = 103 + 0.20 = 103.20

所以AI0的计算是上一期coupon累积了分红周期内已经过去了多长的时间，我理解对吗？那AI（t)又怎么计算呢？accrual interest 都不用折现的吗？至少ai0不用折现，对吧

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1 个答案

Lucky_品职助教 · 2023年03月08日

嗨，爱思考的PZer你好：

答案中给出的S0是0时刻定价，这个公式的原理也可以用于各个时刻定价，比如目前在60时点，就是60时点的bond price + AI60

semi-annual 支付利息的 Treasury，所以每次coupon发放间隔，180天，距离上次发放已经60天，所以要accrue 60天 of 180天的利息。

AI是否需要折现，取决于要算的时点，我们算出的AI正好就是60时点的，就不需要折现了

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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NO.PZ2019010402000057问题如下 Aries is going to purchase a two-yeTreasury notefutures contract, The unrlying 1.2%, semi-annutwo-yeTreasury note isquotea clepriof 103. It hbeen 60 ys sinthe last couponpayment. Aries wants to calculate the full spot priof the unrlying two-yearTreasury note: A.103.60B.103.20C.102.80 B is correct本题考察的是计算一个两年期国库券的价格。S0 = Quotebonpri+ Accrueinterest = + AI0 Accrueinterest ( )= Accrurperio×Perioc coupon amount = （NANT× （C/n）= (60/180) × (0.012*100/2) = 0.20.S0 = 103 + 0.20 = 103.20 按我这个图，上一次发放到settlement，应该是后面三个coupon啊Accrueinterest是指距离上一次coupon发放日到settlement te期间应得的利息。

2023-10-01 23:07 2 · 回答

NO.PZ2019010402000057问题如下 Aries is going to purchase a two-yeTreasury notefutures contract, The unrlying 1.2%, semi-annutwo-yeTreasury note isquotea clepriof 103. It hbeen 60 ys sinthe last couponpayment. Aries wants to calculate the full spot priof the unrlying two-yearTreasury note: A.103.60B.103.20C.102.80 B is correct本题考察的是计算一个两年期国库券的价格。S0 = Quotebonpri+ Accrueinterest = + AI0 Accrueinterest ( )= Accrurperio×Perioc coupon amount = （NANT× （C/n）= (60/180) × (0.012*100/2) = 0.20.S0 = 103 + 0.20 = 103.20 老师这个题里面说他is going to buy，那就说明现在是站在0时点，然后下一句说it hbeen 60ys sinlast coupon payment，那第一次付coupon应该在6个月的时候，那这个表述意思现在就站在8个月的时点了吗？所以没明白让计算spot full pri应该是在哪个时间点上的

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NO.PZ2019010402000057 问题如下 Aries is going to purchase a two-yeTreasury notefutures contract, The unrlying 1.2%, semi-annutwo-yeTreasury note isquotea clepriof 103. It hbeen 60 ys sinthe last couponpayment. Aries wants to calculate the full spot priof the unrlying two-yearTreasury note: A.103.60 B.103.20 C.102.80 B is correct本题考察的是计算一个两年期国库券的价格。S0 = Quotebonpri+ Accrueinterest = + AI0 Accrueinterest ( )= Accrurperio×Perioc coupon amount = （NANT× （C/n）= (60/180) × (0.012*100/2) = 0.20.S0 = 103 + 0.20 = 103.20 老师，答案是= (60/180) × (0.012*100/2)，我自己想的是=60/360*1.2%*100，能否这样计算呢？虽然半年付息，但是60天除以360，是对应年化1.2%的。

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