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· 2022年02月04日

想请问为什么是1.03的三次方呢

  1. FRM I
  2. Financial Markets And Products

NO.PZ2020021204000017

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%.

18个月时6%，按照半年计息难道不应该是（1+6%/3）^3 吗就是1.02的三次方。

求解答，谢谢老师们~

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1 个答案

李坏_品职助教 · 2022年02月07日

嗨，努力学习的PZer你好：


题目里说是semi-annually compounded，每一个利率都得先除以2，再去年化。注意这里18个月利率，说的是18个月之后的远期半年利率为6%，而不是说从现在开始18个月的利率是6%。


比如18个月的利率是6%，那就是(1+6%/2)^3.


24个月利率是6.5%，那应该是（1+6.5%/2)^4

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