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王昕彤 · 2023年02月22日

如题

NO.PZ2019010402000011

问题如下：

A manger entered into a receive-fixed and pay-equity swap three months ago. The annualized fixed rate is 3% and equity index was at 100 when swap was entered. The maturity of swap is one year with quarterly reset, and notional amount is $100 million. The current spot rates are as follows:

Assume the equity index is currently trading at 101, the value of the swap is:

选项：

A.

320,450

B.

246,337

C.

-246,337

解释：

C is correct.

考点：equity swap求value.

解析：

首先画图：

一年期的swap，3个月之前进入的，所以时间轴如下，还剩3笔现金流。

对于equity leg来说，我们可以根据价格水平直接计算现在的value。

${\text{value}}_{equity}=(101/100)\times100,000,000=101,000,000$

对于fixed leg来说，我们只用将三笔现金流折现即可。

$Value_{fixedleg=}3\%\times(\frac{90}{360})\times100000000\times(0.997506+0.992556+0.985222) +100,000,000\times0.985222\\=100,753,663$

Value of swap=-101,000,000+100,753,663=-246,337

老师，为什么equity 不用之后的三个时间点分别折现求出value呢

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Lucky_品职助教 · 2023年02月22日

嗨，努力学习的PZer你好：

本题是站在0.5时点求value，equity value就是股价*数量，根据题目已知条件"Assume the equity index is currently trading at 101",value就是101,000,000，无需折现哦

----------------------------------------------
就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

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