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沐沐的方盒 · 2023年10月23日

没搞清楚方向

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

请问老师,这道题我判断出来是short方,但是我实在没明白为什么最后是负号的?向上箭头(固定)减去向下箭头(equity)是long 的头寸方向,是负数,那short方不就应该是正数的吗?

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已采纳答案

李坏_品职助教 · 2023年10月24日

嗨,努力学习的PZer你好:


对 所有的swap都是这样计算。向上的一律表示收到的现金流,向下的表示支付的现金流。所以value of swap = 收到的现金流现值 - 支付的现金流现值。

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加油吧,让我们一起遇见更好的自己!

李坏_品职助教 · 2023年10月23日

嗨,从没放弃的小努力你好:


这道题说的是收取固定利息、支付equity。


向上箭头是fixed利息部分的现金流,value fixed = 三笔现金流折现 + 一笔本金折现 = 100753663.

向下箭头是equity部分的现金流,value equity = 101/100 * 100000000 = 101000000.


所以对于题目中的这个人来说,他的value = 向上箭头 - 向下箭头 = 100753663 - 101000000 = -246337. 这个数字就是这个Manager的value。


结果是根据向上 - 向下得出来的,不需要额外考虑swap到底是long还是short(swap都是两个方向的现金流,考虑多空意义不大)

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

沐沐的方盒 · 2023年10月24日

是所有swap都用向上箭头减向下箭头就行了吗?不需要再额外考虑对吗?(因为我记得V-LONG是向上减向下,然后V-short是反过来呀)

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