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菱秋秋 · 2021年09月12日

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NO.PZ2018122701000084

问题如下:

With all other things being equal, a risk monitoring system that assumes constant volatility for equity returns will understate the implied volatility for which of the following positions by the largest amount:

选项:

A.

Short position in an at-the-money call

B.

Long position in an at-the-money call

C.

Short position in a deep in-the-money call

D.

Long position in a deep in-the-money call

解释:

D is correct.

考点 Volatility Smile

解析 A plot of the implied volatility of an option as a function of its strike price demonstrates a pattern known as the volatility smile or volatility skew. The implied volatility decreases as the strike price increases. Thus, all else equal, a risk monitoring system which assumes constant volatility for equity returns will understate the implied volatility for a long position in a deep-in-the-money call.

请问答案解析中这句话是什么意思: Thus, all else equal, a risk monitoring system which assumes constant volatility for equity returns will understate the implied volatility for a long position in a deep-in-the-money call.

1 个答案

李坏_品职助教 · 2021年09月13日

嗨,努力学习的PZer你好:


这话的意思是,在假设股票收益率的波动率是常数的前提下,这回低估了深度实值期权的隐含波动率。


考虑一下volatility smile的曲线图,对于深度实值(股票价格远大于strike的)的call,隐含波动率应该是显著大于我们constant volatility的假设的。

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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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