Answer: Short position in a deep out-the-money call

## 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.

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