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410140980 · 2022年11月03日

euqity option的分布

NO.PZ2018122701000083

问题如下:

The Chief Risk Officer of Martingale Investments Group is planning a change in methodology for some of the risk management models used to estimate risk measures. His aim is to move from models that use the normal distribution of returns to models that use the distribution of returns implied by market prices. Martingale Group has a large long position in the German equity stock index DAX which has a volatility smile that slopes downward to the right. How will the change in methodology affect the estimate of expected shortfall (ES)?

选项:

A.

ES with the updated models will be larger than the old estimate.

B.

ES with the updated models will be smaller than the old estimate.

C.

ES will remain unchanged.

D.

Insufficient information to determine.

解释:

A is correct.

考点 Volatility Smile

解析 A volatility smile is a common graphical shape that results from plotting the strike price and implied volatility of a group of options with the same expiration date. Since the volatility smile is downward sloping to the right, the implied distribution has a fatter left tail compared to the lognormal distribution of returns. This means that an extreme decrease in the DAX has a higher probability of occurrence under the implied distribution than the lognormal. The ES will therefore be larger when the methodology is modified.

老师equity option的分布不是左肥右瘦吗?解析当中的意思是左肥右边正常?

1 个答案

李坏_品职助教 · 2022年11月03日

嗨,爱思考的PZer你好:


根据volatility smile的图,应该是左边的implied volatility比较大,所以左侧极端损失的概率大于Lognormal分布,左尾比较肥。


解析并没有提及右边是否正常,一般也不考虑右侧的情况。ES和VaR考虑的都是损失值,只和左尾相关。

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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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