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Weike · 2024年02月19日

最后解释怎么求出的S3不太理解

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。

为什么左边分子都是利率而右边分子都是S3

2 个答案

李坏_品职助教 · 2024年02月20日

嗨,从没放弃的小努力你好:


对,原理是这样的。

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加油吧,让我们一起遇见更好的自己!

李坏_品职助教 · 2024年02月19日

嗨,努力学习的PZer你好:


这个题目的解答可以参考基础班讲义P170-172的例题:


最后那个等式的原理来自于Swap rate的性质:

swap rate可以让投资者的以下两种投资方式等价:

  1. 固定的swap rate利息的现值;
  2. 相应的forward rate的利息现值.


当1和2等价时对应的固定利息就是swap rate。

所以例题最后的公式左侧就是2里面的“相应的forward rate的利息现值”,公式右侧是1里面的固定swap rate利息现值,S3代表的就是3年期的Swap rate。



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虽然现在很辛苦,但努力过的感觉真的很好,加油!

Weike · 2024年02月20日

这个是相当于S3 作为三年期的利率折现到零时刻与每一期的期间利率折现到零时刻是相等的意思么

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