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上小学 · 2023年03月06日

请问此题为何不使用二叉树?使用440页DELTa. ?解题思路是啥?股价的变动可以计算,期权的变动如何计算呢?

NO.PZ2020021205000056

问题如下:

A stock price is currently 40. At the end of six months it will be either 36 or 44. The risk-free rate is 5% per annum with continuous compounding.there is a six month European put option with a strike price of 40,what position should be taken in the stock to hedge a long position in the option?

解释:

The position is long 0.5 shares. This is because 0.5 shares plus the long put option is worth 22 for both outcomes.

讲义上三种解题方法结果相同,但是适用情景有何不同?

1 个答案

pzqa27 · 2023年03月06日

嗨,从没放弃的小努力你好:


请问此题为何不使用二叉树?

二叉树用于对期权的定价,这里问的是如果hedge,不是在问定价,所以不用二叉树

使用440页DELTa. ?

嗯,这里hedge的思想是delta natural

解题思路是啥?

简单来说就是令组合的delta=0,这样组合就可以认为不收到股价变动的线性影响了,题目中现有头寸是long一个put,那么我们只需要long 0.5个股票即可令组合的delta=0

股价的变动可以计算,期权的变动如何计算呢?

期权的价格变动一般就两种方法,一是二叉树,二是BSM,这里不涉及期权价格的变化,这里问的是如何对冲,只需要delta中性即可

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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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