Answer: The call option with a strike price of $40.

## Explanation ### Delta-Normal Approach Limitations: The delta-normal approach assumes linear relationships and is based on: - Using option delta to approximate price changes - Assuming normal distribution of returns ### Why At-the-Money Options Work Best: For the call option with strike price **$40** (at-the-money): 1. **Delta is closest to 0.5**, providing the most accurate linear approximation 2. **Gamma is highest** at-the-money, but the delta-normal approach ignores gamma risk 3. **Linear approximation error is minimized** when the option is not too deep in-the-money or out-of-the-money ### Comparison of Options: - **$35 strike (deep ITM)**: Delta ≈ 1.0, but large gamma makes linear approximation poor - **$40 strike (ATM)**: Delta ≈ 0.5, best balance for linear approximation - **$45 strike (OTM)**: Delta ≈ 0.2-0.3, small delta but large relative errors - **$50 strike (deep OTM)**: Delta ≈ 0.0-0.1, very poor linear approximation ### Conclusion: The **at-the-money option (strike $40)** will have the delta-normal ES closest to the true ES because the linear approximation is most accurate when the option is neither deeply in-the-money nor out-of-the-money.

Author: LeetQuiz Editorial Team