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菱秋秋 · 2021年09月12日

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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.

 move from models that use the normal distribution of returns to models that use the distribution of returns implied by market prices,这样的变动会产生什么影响呢?看不太明白

2 个答案

DD仔_品职助教 · 2021年09月13日

嗨,从没放弃的小努力你好:


同学是的呢~就是这样理解哒

因为implied的volatility图形是左偏的,那就是说损失的数据会更加极端,计算ES是尾部即损失数据的平均,所以会偏高

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DD仔_品职助教 · 2021年09月13日

嗨,爱思考的PZer你好:


同学你好~

他原来用的是正态分布来估计回报率,现在改成用根据市场价格implied的回报率。

正态分布是左右对称的,原本的估计很不符合实际情况。现在改成用实际市场价格计算出来的回报率,直接反应现实,是更容易出现极端情况。我们在估计ES的时候,因为会容易出现极端,所以实际数据估计ES会比用之前的正态分布大。选A

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菱秋秋 · 2021年09月13日

所以因为 equity stock的implied volatility的曲线是left fat tail,所以用左边的数值计算ES会偏高,可以这么理解么?

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