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临江仙 · 2023年10月14日

这题不是short position么

  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.

如果是short forwoard，那么期间的coupon，应该是可以获取的。

为什么要扣减PVCt呢？


而且，S0=1103.45，但是是包含了利息。

为什么不剔除利息呢？

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1 个答案

李坏_品职助教 · 2023年10月14日

嗨，爱思考的PZer你好：


forward是远期合约，债券的利息只有持有债券现货才能得到，远期合约属于衍生品，是拿不到利息的。


公式是F0(T) =  [S0 – PVCI0,T] * (1+rf)^360/360，这里S0是债券的全价（dirty price），公式里面扣除了coupon的现值29.778。然后再按照1.5%的无风险利率求360天之后的forward price。

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