开发者:上海品职教育科技有限公司 隐私政策详情

应用版本:4.2.11(IOS)｜3.2.5(安卓)APP下载

返回

粗眉毛辣椒油 · 2024年03月15日

请问这道题的考点是什么？

  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%.

另外，zero rate不是一般是期限为1年以内债券的到期收益率吗？

添加评论
1 个答案

李坏_品职助教 · 2024年03月16日

嗨，努力学习的PZer你好：


考点是利用即期利率推算远期利率。可以参考讲义P260。讲义里写的是简便算法，本题答案给的是复利计算的精确算法。

题目给的是0-6，0-12，0-18，0-24这个四个时间段的零息债券的利率，所谓的zero rates指的是零息债券的到期收益率。也可以看做是spot rate（即期利率）。

现在让你求出6-12的远期利率、12-18的远期利率、18-24的远期利率.


先看第一个远期利率。既然0-12的spot rate是5.5%，而0-6的spot rate是5%。现在假设6-12的远期利率是r。那么(1+5%/2) * (1+r/2) = (1+5.5%/2)^2，所以r = 0.060012.

第二个远期利率，首先找到0-18的spot rate是6%，而0-12的spot rate是5.5%, 现在假设12-18的远期利率是r，那么(1+5.5% / 2)^2 * (1+r/2) = (1+6%/2)^3， r = 0.070037.


计算远期利率的时候，要按照半年进行复利（semi-annually compounded）。

----------------------------------------------
努力的时光都是限量版，加油！

  • 1

    回答

  • 0

    关注

  • 182

    浏览
相关问题

NO.PZ2020021204000017 问题如下 The six-month, 12-month, 18-month, an24-month zero rates are 5%, 5.5%, 6%, an6.5%, whare the (semi-annually compoun forwarrates for a six-month perio beginning in six, 12, an18 months? The forwarrates are2 X ( 1.02752 /1.025-1) = 0.0600122 X ( 1.033 /1.02752- 1) = 0.0700372 X ( 1.03254 /1.033 - 1)= 0.080073 If all rates were continuously compoun the forwarrates woul6%, 7%, an8%. Because we are aling with a semi-annually compounrate, they are slightly fferent: 6.0012%, 7 .0037%, an8.0073%.

2024-02-28 20:29 1 · 回答

NO.PZ2020021204000017 问题如下 The six-month, 12-month, 18-month, an24-month zero rates are 5%, 5.5%, 6%, an6.5%, whare the (semi-annually compoun forwarrates for a six-month perio beginning in six, 12, an18 months? The forwarrates are2 X ( 1.02752 /1.025-1) = 0.0600122 X ( 1.033 /1.02752- 1) = 0.0700372 X ( 1.03254 /1.033 - 1)= 0.080073 If all rates were continuously compoun the forwarrates woul6%, 7%, an8%. Because we are aling with a semi-annually compounrate, they are slightly fferent: 6.0012%, 7 .0037%, an8.0073%. 问题为什么可以判断题干给的条件，即The six-month, 12-month, 18-month, an24-month zero rates are 5%, 5.5%, 6%, an6.5%, 这些 zero rates也是semi-annually compoun我看题目的意思并没有指出这些是semi-annually compoun只是说forwarrate是semi-annually compound

2023-12-13 17:57 1 · 回答

NO.PZ2020021204000017问题如下The six-month, 12-month, 18-month, an24-month zero rates are 5%, 5.5%, 6%, an6.5%, whare the (semi-annually compoun forwarrates for a six-month perio beginning in six, 12, an18 months? The forwarrates are2 X ( 1.02752 /1.025-1) = 0.0600122 X ( 1.033 /1.02752- 1) = 0.0700372 X ( 1.03254 /1.033 - 1)= 0.080073 If all rates were continuously compoun the forwarrates woul6%, 7%, an8%. Because we are aling with a semi-annually compounrate, they are slightly fferent: 6.0012%, 7 .0037%, an8.0073%. 为什么时间不是0.5，1，1.5计算，而是123？

2023-02-24 23:20 1 · 回答

NO.PZ2020021204000017 问题如下 The six-month, 12-month, 18-month, an24-month zero rates are 5%, 5.5%, 6%, an6.5%, whare the (semi-annually compoun forwarrates for a six-month perio beginning in six, 12, an18 months? The forwarrates are2 X ( 1.02752 /1.025-1) = 0.0600122 X ( 1.033 /1.02752- 1) = 0.0700372 X ( 1.03254 /1.033 - 1)= 0.080073 If all rates were continuously compoun the forwarrates woul6%, 7%, an8%. Because we are aling with a semi-annually compounrate, they are slightly fferent: 6.0012%, 7 .0037%, an8.0073%. 李老师讲的公式是R1*T1+Rfowar（T2-T1）=R2*T2，但答案是（1+R1）*T1*（1+Rforwar*（T2-T1）=（1+R2）^2*T2可以具体一下为什么吗 两个公式分别适用于什么情况

2023-02-12 18:46 2 · 回答