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.
明白这一题考的是equity 波动率微笑，但波动率微笑y轴是隐含波动率，x轴是执行价格。求ES图形，x轴是损失值，y轴是概率。波动率微笑图形如何得出ES的判断？
