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.
对于equity，分布相对于lognornal来说是左肥右瘦的，那么如何确定该指数是大于执行价格还是小于执行价格？