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游游 · 2024年10月20日

零息的YTM

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?

1 个答案
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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