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良爱洳 · 2021年07月20日

问一道题:NO.PZ2016070202000026 [ FRM II ]

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).

为什么在strike price附近波动 期权就最profitable?而不是选B!
1 个答案

品职答疑小助手雍 · 2021年07月20日

嗨,爱思考的PZer你好:


这题考的不是期权利润而是动态对冲的理念,ATM的option的delta大致是在0.5的,这时候gamma最大,一旦underlying上升或者下降,ITM或者OTM的option的delta都会有显著变化,导致对冲的头寸需要调整,增加成本,而一直围绕行权价波动的话,delta一直是0.5左右,对冲的头寸比较稳定,成本就比较低。

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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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