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Caroline123456 · 2024年04月08日

为什么coupon的计算是用90跟270，而不是180跟360

  1. CFA II
  2. Derivative

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.

为什么coupon的计算是用90跟270，而不是180跟360

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已采纳答案

pzqa35 · 2024年04月10日

嗨，爱思考的PZer你好：


题目中是说他买了一个bond，然后想要hedge这个bond的风险，因此有人建议他short一个forward，并且说了市面上的一个forward的特征。但是题目问的是“the price of the forward contract on the bond purchased by Kim is closest to”，也就是说以他买的这个bond为标的资产的forward价格应该是多少，所以应该是按照他买的这个bond的特征去计算forward的定价。

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努力的时光都是限量版，加油！

pzqa35 · 2024年04月09日

嗨，爱思考的PZer你好：


这里有个时间点需要注意的就是债券是在90天之前买入的，那么当前是0时刻，下一个coupon日就是90天。

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努力的时光都是限量版，加油！

Caroline123456 · 2024年04月09日

可是现在这个bond是新的啊，为什么要用原来的bond的coupon

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