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Carolyne · 2024年04月24日

小变动

NO.PZ2023041003000058

问题如下:

Burr asks Madisox to outline an appropriate hedging strategy. Madisox replies that to be fully hedged, an option trader will need to consider how changes in the stock price relative to the option exercise price affect the value of the call options. To be fully hedged against a small change in the stock price, Madisox suggests that the proper strategy to construct the hedge is to use call option delta and add the call option gamma to arrive at the number of shares required.

Is Madisox’s suggested hedging strategy for Weehawkin options most likely correct?

选项:

A.

Yes

B.

No, he should only use delta.

C.

No, he should subtract gamma.

解释:

Madisox’s statement is correct. To be fully hedged against a small change in the stock price, the proper strategy to construct the hedge is to use call option delta and add the call option gamma to arrive at the number of shares required. The number of shares required is 0.606, based on the option delta of 0.587 plus the option gamma of 0.019.

B is incorrect. To be fully hedged against a small change in the stock price, the proper strategy to construct the hedge is to use call option delta and add the call option gamma to arrive at the number of shares required.

C is incorrect. You need to add, not subtract, option gamma to the option delta.

小幅变动不是说只用delta 就可以了嘛

1 个答案

李坏_品职助教 · 2024年04月24日

嗨,爱思考的PZer你好:


这个题目是要求小幅变动的情况下要保证delta的完全对冲,但是由于gamma的存在,delta是不稳定的,所以要想严格的fully hedged,必须把gamma也加到delta里面。


可以参考基础班讲义关于Gamma的介绍,当股票价格小幅变化时,Gamma会导致delta产生变动。


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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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2023-08-16 18:00 2 · 回答