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12345678wdv · 2024年05月01日

为什么 P 不用折现后的数值,而是用原值 420

NO.PZ2023091802000100

问题如下:

A trader executes a $420 million 5-year pay fixed swap (duration 4.433) with one client and a $385 million 10 year receive fixed swap (duration 7.581) with another client shortly afterwards. Assuming that the 5-year rate is 4.15% and 10-year rate is 5.38% and that all contracts are transacted at par, how can the trader hedge his position?

选项:

A.

Buy 4,227 Eurodollar contracts

B.

Sell 4,227 Eurodollar contracts

C.

Buy 7,185 Eurodollar contracts

D.

Sell 7,185 Eurodollar contracts

解释:

Step1. First swap is equivalent to a short position in a bond with similar coupon characteristics and maturity offset by a long position in a floating-rate note.

Its

Step2. Second swap is equivalent to a long position in a bond with similar coupon characteristics and maturity offset by a short position in a floating-rate note.

Its

Step3. Net DV01 of portfolio = -0.186+ 0.291 = 0.105m = 105,683

Step4. The optimal number is (Note that the DVBP of the Eurodollar futures is about 25.)


如题

1 个答案

李坏_品职助教 · 2024年05月02日

嗨,努力学习的PZer你好:


这题首先计算的是两个swap合约的DV01,DV01表示当利率变动0.01%时,债券价值的变动金额。


swap合约在期初可以看做是两只债券,一个是固定利息债券,一个是浮动利息债券。浮动利息债券在期初的久期=0,所以Swap的久期就是固定利息债券的久期。而题目后面告诉我们“ all contracts are transacted at par”,意思是交易价格=面值,所以420就是这个swap包含的固定利息债券的价格,不需要折现。

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努力的时光都是限量版,加油!

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