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YAO Monica · 2024年03月24日

90时间点是在节点,为什么不是按照节点计算CFs计算而是按照整体求value?

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。

valueequity=(101/100)×100,000,000=101,000,000{\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。

Valuefixedleg=3%×(90360)×100000000×(0.997506+0.992556+0.985222)+100,000,000×0.985222=100,753,663Value_{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

90时间点是在节点,可以求两个

1)节点处CFs的(互换收益率)

2)节点处的value(互换整体,bond部分是折现(未来的现金流+NP))

是这么理解吗?

1 个答案
已采纳答案

李坏_品职助教 · 2024年03月24日

嗨,从没放弃的小努力你好:


题目最后问的是 the value of the swap(收固定、支付equity),我们需要把固定利率部分的value求出来,再把equity部分的value求出来,作差即可。


注意equity部分是不存在每个节点的现金流,它是直接用现在的股票指数价格101除以本金100,再乘以面值100million,这个直接作为value。

固定利率部分是按照后期每一个CF都折现到90时间点,作为value。



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虽然现在很辛苦,但努力过的感觉真的很好,加油!

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