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miao999 · 2022年02月09日

为什么连题干中给的zero rates也要变成半年复利一次啊，题干不是只要求forward rate是半年复利一次吗

  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%.

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?

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2 个答案

DD仔_品职助教 · 2023年03月20日

嗨，从没放弃的小努力你好：


答案是6.0012%，计算器要设置为6位小数

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DD仔_品职助教 · 2022年02月09日

嗨，努力学习的PZer你好：


同学你好，

这里虽然没有说清楚zero rate也是半年付息一次，但是一般情况都是相互对应的，要求求的是半年付息一次的forward rate，那么对应的zero rate也是半年付息一次的。

我们以第一个forward rate为例(如下图)，虽然给出来的就是半年期的利率，但是这个利率是以年的形式表示的，所以要把时间进行调整，不然没有办法求远期利率。

反求f0.5-->1=0.060012


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Dearkerry · 2023年03月20日

老师，按照您上面写的公式计算下来，应该是6%呀？

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