Explanation

When a risk monitoring system assumes constant volatility (ignoring the volatility smile/skew), it will understate implied volatility most significantly for deep out-of-the-money options.

Key Concepts:

1. Volatility Smile/Skew: In equity markets, implied volatility tends to be higher for deep out-of-the-money options and deep in-the-money options compared to at-the-money options.

2. Why Deep OTM Calls Have Higher Implied Volatility:

   • Deep OTM calls have low probability of expiring in-the-money
   • Higher implied volatility reflects the market's expectation of potential large price moves
   • This creates a volatility "smirk" where OTM calls have higher implied volatility than ATM options

3. Impact of Constant Volatility Assumption:

   • A system assuming constant volatility would use the same volatility for all strike prices
   • This would understate the actual implied volatility for deep OTM calls by the largest amount
   • For ATM options, the difference would be smaller
   • For deep ITM options, the volatility difference is also smaller

4. Position Analysis:

   • Short position in deep OTM call (Option C): The system would underestimate the volatility risk premium, potentially underpricing the option and underestimating the risk of the short position
   • This represents the largest understatement because deep OTM options exhibit the greatest deviation from constant volatility assumptions

Therefore, the short position in a deep out-the-money call would experience the largest understatement of implied volatility when using a constant volatility model.