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台风来了 · 2023年06月30日

关于receive-fixed and pay-equity swap的现金流

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，您好！从计算过程看，对于这样一个收固定利率并支付equity的swap，现金流除了每期固定利率的coupon外，最后还发生了本金的互换，包括股票。是这样吗？我理解的这个互换，对于题目中描述的投资者，应该是每期收到fixed rate coupon，并支付每期股价对于初始价格的价差带来的损益，即最后不涉及本金的互换。麻烦老师解释一下，谢谢！

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Lucky_品职助教 · 2023年07月01日

嗨，爱思考的PZer你好：

是的，最后是现金轧差结算，不涉及本金和股票的互换。

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努力的时光都是限量版，加油！

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