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PZmomo · 2024年02月04日

为什么不考虑AIT?

NO.PZ2023020101000010

问题如下:

Three months ago (90 days), Kim purchased a bond with a 3% annual coupon and a maturity date of seven years from the date of purchase. The bond has a face value of US$1,000 and pays interest every 180 days from the date of issue. Kim is concerned about a potential increase in interest rates over the next year and has approached Riley for advice on how to use forward contracts to manage this risk. Riley advises Kim to enter into a short position in a fixed-income forward contract expiring in 360 days. The annualized risk-free rate now is 1.5% per year and the price of the bond with accrued interest is US$1,103.45.

Based on a 360-day year, the price of the forward contract on the bond purchased by Kim is closest to

选项:

A.

US$1,082.

B.

US$1,090.

C.

US$1,120.

解释:

Note that time 0 is the forward contract initiation date, that is, 90 days after the purchase of the bond. Time T is the contract expiration date, that is, 360 days.

The forward contract price follows:

F0(T) = FV0,T [S0 – PVCI0,T]

Present value (PV) of coupons = PVCI0,T = 15/(1.015)90/360 + 15/(1.015)270/360 = 14.944 + 14.833 = US$29.778

F0(T) = (1103.45 – 29.778)(1.015)360/360 = US$1,090.

之前有老师回答了这个问题,这个回答不是特别理解:

Lucky_品职助教 · 2023/7/2 21:07:51

嗨,努力学习的PZer你好:

F0(T) = FV0,T [S0 – PVCI0,T] 计算forward合约价值,不涉及AIT哦,那是计算futures的公式


forward和futures在计算price时有什么区别?是说forward作为非标准化的产品,其报价就包含了AIT吗?

2 个答案

李坏_品职助教 · 2024年03月10日

嗨,爱思考的PZer你好:


Futures price的公式在CFA二级的Derivatives 讲义P45:

计算futures price要扣除AIT。


而Forward因为不是在交易所交易的,所以不用扣除AIT。Forward price只需要考虑合约期间资产的收益或成本,公式可以参考CFA一级衍生品的讲义:

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

李坏_品职助教 · 2024年02月04日

嗨,从没放弃的小努力你好:


futures报价和债券现货的规定是一样的,都是用clean price(净价)报价,所以futures price需要减去AIT。


但forward因为是定制化产品,不需要服从交易所的规定,不用clean price报价,也就不用扣减AIT。

----------------------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!

yycfa · 2024年03月10日

请问这个小的知识点,在讲义的什么地方,谢谢

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