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yuqijeffery · 2021年03月12日

不太明白为什么spot等于前面三个forward rate乘在一起

  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%

不太明白为什么spot等于前面三个forward rate乘在一起

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1 个答案

吴昊_品职助教 · 2021年03月12日

嗨，努力学习的PZer你好：


同学你好：

这道题是通过forward rate反求spot rate。用到的是殊途同归的方法。

式子左边：代表的是一次性投资一年，用到的利率是f(0,1)，其实也是S1，此时时间来到了第一年末；再投资一年，用的是远期利率f（1,1），此时时间来到了第二年末；再投资一年，用的是远期利率f(2,1)，（代表的就是2时间开始的一年期远期利率），此时时间来到了第三年末。投资结束后时间正好到第三年末。和式子的右边一次性投资三年获得的收益率应该是一样的。这样就把远期利率和即期利率关联起来了。

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努力的时光都是限量版，加油！

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