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莫等闲2023 · 2020年03月15日

问一道题：NO.PZ2020021204000017

  1. FRM I
  2. Financial Markets And Products

问题如下：

The six-month, 12-month, 18-month, and 24-month zero rates are 5%, 5.5%, 6%, and 6.5%, what are the (semi-annually compounded) forward rates for a six-month periods beginning in six, 12, and 18 months?

选项：

解释：

The forward rates are

2 X ( 1.02752 /1.025-1) = 0.060012

2 X ( 1.033 /1.02752- 1) = 0.070037

2 X ( 1.03254 /1.033 - 1)= 0.080073

If all rates were continuously compounded, the forward rates would be 6%, 7%, and 8%. Because we are dealing with a semi-annually compounded rate, they are slightly different: 6.0012%, 7 .0037%, and 8.0073%.

老师能详细讲一下这道题的推导么？为什么我算出来是7%，7.5%和8%

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1 个答案

袁园_品职助教 · 2020年03月16日

同学你好！

题目中给的都是年化的利息，semi-annually compounded 的时候需要除以2

以 f(6,12) 为例：

(1+S6/2)*(1+f(6,12)/2)=(1+S12/2)^2

(1+5%/2)*(1+f(6,12))=(1+5.5%/2)^2

f(6,12)=6.0012%

你可以自己试着算下剩下两个。

下次可以把你自己的计算过程也放上来提问，这样可以帮你找出错误的地方，加油！

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