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luckygrace · 2024年04月05日

等式右面为啥都是S3

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。

请问等式右面为啥都是s3,而不是s1 s2 s3

2 个答案

pzqa35 · 2024年04月07日

嗨,爱思考的PZer你好:


我们在对swap进行定价的时候只是把它看成了两个债券的互换,但是这个coupon的理解我觉得从计算角度来看是完全可以的,而且比较好记哈。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

pzqa35 · 2024年04月07日

嗨,从没放弃的小努力你好:


这个s代表的是swap rate,swap rate是我们在互换时定的那个固定利率,因此是固定不变的哈。

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加油吧,让我们一起遇见更好的自己!

luckygrace · 2024年04月07日

这个swap rate其实就是coupon对吗?

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