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yinyincat · 2020年03月31日

问一道题:NO.PZ2019010402000012

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:

The value of this equity swap would be zero if the equity index level is:

选项:

A.

100.753630

B.

100

C.

99.753630

解释:

A is correct.

考点:equity swap求value

解析:

已知value=0,反求此时equity index的价格。

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

将现在index的价格设为X,那么equity leg的价值=X/100*100,000,000

头寸是付equity return收固定,所以value of swap=- X/100*100,000,000+100,753,630=0

可计算出X=100.753630

老师,

为什么equity value 是x/100xNP,而不是(x-100)xNP呢?

2 个答案
已采纳答案

xiaowan_品职助教 · 2020年03月31日

同学你好,因NP代表名义本金,而不是代表买了多少股,这道题目中股票指数初始价格是100,x/100代表现在这个价格是初始价格的多少倍,相应的value也是初始本金的多少倍

xiaowan_品职助教 · 2020年03月31日

嗨,爱思考的PZer你好:


同学你好,因为x-100是只计算增值的部分,而我们在固定端是要将本金也折现到当前时刻的,这样子两边就不匹配了,

所以用x/100,得到的是包括本金的值。


-------------------------------
虽然现在很辛苦,但努力过的感觉真的很好,加油!


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