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游游 · 2024年10月20日

零息的YTM

  1. FRM I
  2. Financial Markets And Products

NO.PZ2023091802000084

问题如下：

Given the following bonds and forward rates:

1-year forward rate one year from today = 9.56%

1-year forward rate two years from today = 10.77%

2-year forward rate one year from today = 11.32%

Which of the following statements about the forward rates, based on the bond prices, is true?

选项：

A.

The 1-year forward rate one year from today is too low.

B.

The 2-year forward rate one year from today is too high.

C.

The 1-year forward rate two years from today is too low.

D.

The forward rates and bond prices provide no opportunities for arbitrage.

解释：

1-year forward rate one year from today = 1.072/1.045 – 1 = 9.56%

1-year forward rate two years from today = 1.093/1.072 – 1 = 13.11%

2-year forward rate one year from today = (1.093/1.045)0.5 – 1 = 11.32%

是不是可以理解为零息债券的YTM与spot rate就是一样的？

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已采纳答案

pzqa39 · 2024年10月21日

嗨，努力学习的PZer你好：


是的，可以这么理解，由于零息债券没有中间的现金流（利息支付），它的唯一现金流是到期时的面值支付，因此，投资者购买零息债券的回报完全来自于到期时的面值。为了计算债券的现值，我们需要使用即期利率来折现到期时的面值。因此，零息债券的 YTM 实际上就是与其相对应期限的即期利率。

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