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Fair · 2022年01月26日

看完解析还是云里雾里不懂,能否整条题目重新梳理说一说?

NO.PZ2016070202000026

问题如下:

A trader buys an at-the-money call option with the intention of delta-hedging it to maturity. Which one of the following is likely to be the most profitable over the life of the option?

选项:

A.

An increase in implied volatility

B.

The underlying price steadily rising over the life of the option

C.

The underlying price steadily decreasing over the life of the option

D.

The underlying price drifting back and forth around the strike over the life of the option

解释:

D is correct. An important aspect of the question is the fact that the option is held to maturity. Answer A is incorrect because changes in the implied volatility would change the value of the option, but this has no effect when holding to maturity. The profit from the dynamic portfolio will depend on whether the actual volatility differs from the initial implied volatility. It does not depend on whether the option ends up in-the-money, so answers B and B are incorrect. The portfolio will be profitable if the actual volatility is small, which implies small moves around the strike price (answer D).

看完解析还是云里雾里不懂,能否整条题目重新梳理说一说?

2 个答案

李坏_品职助教 · 2023年07月01日

嗨,爱思考的PZer你好:


是从动态调整的成本考虑的。

这个题目说的delta对冲是指:买入期权作为对冲工具,目的是让期权和原来的资产(比如股票)组合起来之后的delta等于0。

而Delta对冲是个需要不断调整仓位的动态过程。如果标的资产的真实波动率过大,那么每次调整期权数量的幅度就会很大,就会带来很高的调仓成本。因此,真实波动率越小(也就是股票价格围绕着行权价格小幅变动,back and forth around the strike),动态调整成本也越小,即越profitable。


implied volatility增加,期权的价值会上升,但问题是这道题说的是to maturity——持有期权到期,所以未到期之前的期权升值跟你没有什么关系(就是不考虑提前行权)。


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李坏_品职助教 · 2022年01月27日

嗨,爱思考的PZer你好:


题干说的是,一个交易员买了一份平值期权,他对这份期权进行了delta hedge,一直持有到期。下面哪一项最有可能使得这个交易员获利?


这道题可以从delta hedge,也就是期权对冲的成本来考虑。注意题目说的是持有到期,所以implied volatility的增加只会让期权立刻升值,不会影响到期日的期权价值,所以不会让交易员在期权到期日获利。不选A。


平值期权的option的delta大致是在0.5的,这时候gamma最大。一旦股票价格上升或者下降,option的delta都会有显著变化,导致对冲的头寸需要调整,增加对冲成本。而如果股票价格一直围绕行权价波动的话,delta一直是0.5左右,对冲的头寸几乎不用调整,成本就比较低。所以D是正确的。

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410140980 · 2023年07月01日

老师看了你这边的解释,我理解的这道题是从成本角度去考虑交易员是否获利? 另外还有个困惑是implied volatility的增加只会让期权立刻升值,不会影响到期日的期权价值,这个怎么理解?

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