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C_M_ · 2024年09月25日

fat tail

NO.PZ2023100703000109

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 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.

为什么downward sloping to the right可以看出是左肥右瘦的分布

1 个答案

李坏_品职助教 · 2024年09月26日

嗨,从没放弃的小努力你好:


因为横坐标是strike price。从左上方向右下方倾斜,表示strike price低的时候volatility很大,而price高的时候volatility比较低。


意思是股价低的时候对应的波动率更大,比较容易出现极端的负收益(就是暴跌概率大)。股价高的时候反而波动低,不太会出现极端的正收益(暴涨概率低)。所以是左尾(暴跌区间)更肥。

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NO.PZ2023100703000109问题如下The Chief Risk Officer of Martingale Investments Group is planning a change in methology for some of the risk management mols useto estimate risk measures. His aim is to move from mols thuse the normstribution of returns to mols thuse the stribution of returns impliemarket prices. Martingale Group ha large long position in the Germequity stoinx X whiha volatility smile thslopes wnwarto the right. How will the change in methology affethe estimate of expecteshortfall (ES)?A.ES with the uptemols will larger ththe olestimate.B.ES with the uptemols will smaller ththe olestimate.C.ES will remain unchangeInsufficient information to termine.A volatility smile is a common graphicshape thresults from plotting the strike prianimplievolatility of a group of options with the same expiration te. Sinthe volatility smile is wnwarsloping to the right, the impliestribution ha fatter left tail compareto the lognormstribution of returns. This means thextreme crease in the X ha higher probability of occurrenunr the impliestribution ththe lognormal. The ES will therefore larger when the methology is mofie没懂这个“因为横坐标是strike price。从左上方向右下方倾斜,表示strike price低的时候volatility很大,而price高的时候volatility比较低。意思是股价低的时候对应的波动率更大,比较容易出现极端的负收益(就是暴跌概率大)。股价高的时候反而波动低,不太会出现极端的正收益(暴涨概率低)。所以是左尾(暴跌区间)更肥。”题目只说了long call 没说是ITM还是OTM的call,分别是隐含波动率的左侧(波动率高)和右侧(波动率低),如果是ITM ES更大没问题,但如果是OTM,波动率低,ES应该更小啊。

2025-07-31 21:11 1 · 回答