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Ash · 2022年10月02日

利率

  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。

为什么不是从1y1y开始，到3y1y? 0y1y 不是0时刻的利率吗

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1 个答案

吴昊_品职助教 · 2022年10月08日

嗨，努力学习的PZer你好：


0y1y代表的是0时间开始一年期的远期利率，也就是S1.

[1+f(0y1y)]×[1+f(1y1y)]×[1+f(2y1y)]这个式子，代表的是从0时间点开始往后滚三年。刚好就等于左边用S3直接一次性投资三年。

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