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Gabriela · 2024年09月08日

zero rate ,spot rate 与IFR 的区别

NO.PZ2021061002000052

问题如下:

QWR is a financial intermediary active in both futures and forward markets. At time t = 0, QWR observes the following zero rates over three periods:


About the three-period par swap rate (S3), Which of the following descriptions is correct?

选项:

A.

Because the swap rate represents the fixed rate at which the present value of fixed and future cash flows equal one another, we can first use zero rates to solve for the implied forward rate per period, then discount each implied forward rate back to the present using zero rates, and solve for s3 to get 3.46%.

B.

Because the swap rate represents the fixed rate at which the present value of fixed and future cash flows equal one another, we can use zero rates to discount each zero rate back to the present, and solve for s3 to get 3.02%.

C.

Because the swap rate represents the fixed rate at which the present value of fixed and future cash flows equal one another, we can first use zero rates to solve for the implied forward rate per period, then discount each zero rate back to the present using implied forward rates, and solve for s3 to get 3.99%

解释:

中文解析

本题考察的实际是“脱靴(bootstrapping)”的过程。

具体计算如下:

先根据下面的公式计算出:

IFR0,1 = 2.52%, IFR1,1 = 3.56%, and IFR2,1 = 4.43%


然后再按照下面的公式计算S3:



最终得到S3 =3.46%,选A。

如题,该题中涉及到的几个利率分别怎么区别,定义有什么不一样?S3不是spot rate 3吗? S3是什么?

1 个答案

李坏_品职助教 · 2024年09月08日

嗨,从没放弃的小努力你好:


建议同学回去把这个视频课(基础班)再看一下:


题目里的S指的不是spot rate,而是swap rate。


spot rate: 也叫做zero rate(对应题目里的zero rates,表格给出的条件),他是不同期限的即期利率。

IFR:这个是根据不同的zero rates推算出来的各个时间段内的远期利率(基础班讲义P137-138)。

而swap rate指的是某个年限的利率,比如S3指的是3年期的Swap rate。这个利率可以使得IFR的折现之和 = swap rate的折现之和,折现率都是zero rate。

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