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哇哈哈哈 · 2024年09月19日

这道题如何看出来是Long stock + Long put

NO.PZ2023041003000051

问题如下:

Lee also indicates that a long position in puts could be used to hedge larger moves in the GPX. She notes that although hedging with either puts or calls can result in a delta-neutral position, they would need to consider the resulting gamma.

Lee’s put-based hedge strategy for Solomon’s ETF position would most likely result in a portfolio gamma that is:

选项:

A.

negative.

B.

neutral.

C.

positive.

解释:

Because the gamma of the stock position is 0 and the put gamma is always non-negative, adding a long position in put options would most likely result in a positive portfolio gamma.

Gamma is the change in delta from a small change in the stock’s value. A stock position always has a delta of +1. Because the delta does not change, gamma equals 0.

The gamma of a call equals the gamma of a similar put, which can be proven using put-call parity.

如题: 这道题如何看出来是Long stock + Long put

1 个答案

李坏_品职助教 · 2024年09月19日

嗨,从没放弃的小努力你好:


题目一开始说的是a long position in puts could be used,说明这个是考虑用long put进行hedge。


也就是本来手里有stock,现在加上了long put。这样的话,由于stock的gamma为0,而long put会带来正的gamma,所以组合起来之后的gamma大于0. 题目问的就是组合起来的gamma会怎样?最后选C。


本题和call没什么关系,答案里面说的意思是,put option的gamma与相同行权价的call option是一样的,这个可以用put-call parity定理进行证明(这个证明过程与本题无关)。


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努力的时光都是限量版,加油!

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