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DDup · 2023年01月06日

为什么要对利率折现

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。

为什么要对利率折现,我觉得很莫名其妙,一般折现的都是金额吧


这道题的整个解法,我都不太懂原因


(我已经看过答案了,不要给我复制一遍答案当作回答…

1 个答案

Lucky_品职助教 · 2023年01月06日

嗨,爱思考的PZer你好:


我们假设期初是1块钱,(1+利率)再乘以时间的复利,算出来的是金额,不是单纯对利率折现

本题题目给的利率是0-1,0-2,0-3的利率,问的是par rate即0-1,1-2,2-3的利率,同样1块钱,从0-1和1-2复利得到的金额(存一年后再存一年),应该和0-2复利得到的金额(直接存两年)是一样的,bootstrapping用的就是这个原理~

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