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AgnesWu · 2023年01月19日

没有看懂最后求S3恒等式

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。

能算出来3个IFR,但没有看懂最后求S3恒等式,请老师讲解

1 个答案
已采纳答案

Lucky_品职助教 · 2023年01月24日

嗨,努力学习的PZer你好:


本题题目给的利率是0-1,0-2,0-3的利率,问的是par swap rate,我们通过先求1-2,2-3的forward rate,再求出par swap rate,因为同样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~

S3求解公式左侧是0-1,1-2,2-3分区间并按照区间利率进行折现,右侧是0-3区间,假定都是同一利率S3,从而算出这个S3的值

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努力的时光都是限量版,加油!

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