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JiangHan · 2023年02月12日

由spot rate求forward rate的一道题

  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%.

李老师讲的公式是R1*T1+Rfoward*（T2-T1）=R2*T2，但答案是（1+R1）*T1*（1+Rforward）*（T2-T1）=（1+R2）^2*T2

可以具体解释一下为什么吗 两个公式分别适用于什么情况

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已采纳答案

pzqa27 · 2023年02月13日

嗨，努力学习的PZer你好：


李斯克那个公式适用于连续型复利

答案这个是离散型复利

R1*T1+Rfoward*（T2-T1）=R2*T2，这个的原型是e^R1T1*e^[F(T2-T1)]=e^R2T2

然后等号左右两边取对数即可得到，这里连续型复利

解析这个是离散型复利。题里说了(semi-annually compounded，故判断不是连续型复利，所以用离散型

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

JiangHan · 2023年02月13日

可是当时李老师讲得连续型和离散型复利都是这一个式子啊，离散型的话，是把时间看作权重，也是同样的式子

pzqa27 · 2023年02月14日

嗨，从没放弃的小努力你好：


可是当时李老师讲得连续型和离散型复利都是这一个式子啊，离散型的话，是把时间看作权重，也是同样的式子

好像不是吧，这里版书很明确地写着，只有连续利率才成立

这个图明确写着是离散的情况

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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