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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

  1. FRM I
  2. Financial Markets And Products

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.)


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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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