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Summer. · 2021年10月06日

不明白代哪个公式

  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%.

这是代T1*R1+（T2-T1）Rf=T2*R2的公式吗？


老师能看一下我写的计算吗，错哪？以及这样的方程怎么按计算器啊，用计算器的时候都需要先吧（1+5%）0.5先运算完再记下来，再算右边的式子，可以指点一下怎么按计算器吗，看了计算器的视频也没明白。

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品职答疑小助手雍 · 2021年10月08日

同学你好，我觉得你的公式错误的点不是时间轴的问题，是没有明白复利的含义。所以没必要画时间轴。

我举个例子你类比一下，1年期债券半年付息一次，年化收益率6%，你计算过程肯定是1.03的平方，但是它的来源其实是(1+6%/2)乘以(1+6%/2)对吧，本题和这个例子同理：

你写了个(1+R半年/2)的0.5次方，这里是不对的，对比你会发现不需要再0.5次方了。

而等式右边其实就跟我前面举的例子一样，变个数字，应该是1.0275的平方。

品职答疑小助手雍 · 2021年10月07日

同学你好，你公式写错了，如果用复利的话，除以2就已经代表半年了，不用再0.5次方了。复利的用法是（半年期复利的话）1年期的实际利率等于(1+R/2)^2。意思是以半年为期复利2次（这就等于1年了）


所以求6-12个月的forward 应该是(1+R0.5/2)乘以(1+RF/2) 等于(1+R1/2)的2次方。即(1+2.5%)*(1+RF/2)=(1+2.75%)^2

Summer. · 2021年10月08日

老师好，能不能画个时间轴的图让我看一下，这里还是没听懂。谢谢老师。

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