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Sofia nice · 2024年04月26日

The 3-year implied spot rate的理解

  1. CFA I
  2. Fixed Income

NO.PZ2016031001000088

问题如下：


All rates are annual rates stated for a periodicity of one (effective annual rates).

The 3-year implied spot rate is closest to:

选项：

A.

1.18%.

B.

1.94%.

C.

2.28%.

解释：

B is correct.

The 3 year implied spot rate is closest to 1.94%. It is calculated as the geometric average of the one-year forward rates:

(1.0080 × 1.0112 × 1.0394) = (1 + z3)3

1.05945 =(1+Z3)3

[1.05945]1/3= [(1+Z3)3] 1/3

1.01944 = 1 + z3

1.01944-1 = z3

0.01944 = z3, z3 = 1.944% or approximately 1.94%

考点：spot rate & forward rate

解析：(1+S3 )3 =[1+f(0y1y)]×[1+f(1y1y)]×[1+f(2y1y)]，把表格内的数据代入公式的右边，就可以反求出S3 =1.94%，故选项B正确。

老师，这道题，很多时候是错在这个英文理解上The 3-year implied spot rate，是代表什么，是哪个三年期。这个英文表述能否规范介绍下。有的同学会觉得，为啥不是1年往后的算三年，而是0年开始算三年

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吴昊_品职助教 · 2024年04月26日

嗨，爱思考的PZer你好：


只要是spot rate，都是站在零时刻的即期利率，不会是站在一年后的利率。站在未来时间点的利率是远期利率，而不是即期利率。

这里有两个概念：  

1、即期利率指站在零时间点上，观察到的未来一段时间的利率水平。比如在“T=0”时刻，观察到的未来一年期的利率水平就是1年期的即期利率，记作S1或者Z1

2、远期利率是指站在将来某一个时间点，观察到这一时间点之后一段时间的利率水平。比如站在1时刻，往后的两年期远期利率，我们就记作1y2y。

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