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sabrinababe · 2022年01月17日

式子的左边等于1是什么原理？

  1. CFA II
  2. Fixed Income

NO.PZ2018123101000018

问题如下：

Jane is a bond trader for an investment bank. Exhibit 1 presents the current par and spot rates.

Note: Par and spot rates are based on annual-coupon sovereign bonds.

Based on Exhibit 1, the five-year spot rate is closest to:

选项：

A.

4.40%

B.

4.45%

C.

4.50%

解释：

B is correct.

考点：The Swap Rate Curve和Spot rate的关系

解析：

已知1-year, 2-year, 3-year, 4-year的Spot rate，也知道5-year的Swap rate，根据由Swap rate求Spot rate的方法，有公式：

1=0.0437/(1.025)+0.0437/(1.03)^2+0.0437/(1.035)^3+0.0437/(1.04)^4+1.0437/(1+S5)^5

S5=4.45%

式子的左边等于1是什么原理？如果考试考的话会怎么考（这个等于1的理论）？

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1 个答案

pzqa015 · 2022年01月18日

嗨，努力学习的PZer你好：


这道题考察的是par rate和spot rate之间的关系

5年期spot rate计算方法如下：

par=coupon5/(1+s1)+coupon5/(1+s2)^2+coupon5/(1+s3)^3+coupon5/(1+s4)^4+(coupon5+par)/(1+s5)^5


100=4.37/(1+2.5%)+4.37/(1+3%)+4.37/(1+3.5%)+4.37/(1+4%)+104.37/(1+s5)^5,

等号两边同时除以100后，就是解析中的公式，等式左边为1.

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