Explanation

When a volatility smile slopes downward to the right (also known as a reverse skew), it indicates that:

• Out-of-the-money (OTM) put options (which protect against downside risk) have higher implied volatility than at-the-money (ATM) or out-of-the-money call options.
• This pattern is common in equity markets where investors are willing to pay more for downside protection, leading to higher implied volatility for OTM puts.

Key Points:

1. Long position in DAX: The firm is exposed to downside risk (market declines).
2. Volatility smile sloping downward to the right: Higher implied volatility for OTM puts suggests the market expects larger tail losses than a normal distribution would imply.
3. Change in methodology: Using the distribution of returns implied by market prices (rather than historical or normal distributions) will incorporate this market-implied tail risk.

Impact on Expected Shortfall (ES):

• Expected Shortfall (ES) measures the average loss in the worst-case scenarios (beyond VaR).
• When using market-implied distributions that account for higher tail risk (due to the volatility smile), the estimated ES will increase because:
  • The distribution has fatter tails (higher probability of extreme losses).
  • The average loss in the worst cases will be larger.

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

Correct Answer: A