Explanation

The delta-normal model works best for linear portfolios and serves as an approximation for non-linear portfolios such as option positions. This approximation is reasonable when curvature (as measured by gamma) is low, but becomes less accurate as gamma increases.

Key Analysis:

• Gamma characteristics: Gamma is lower for options that are deep in-the-money or deep out-of-the-money compared to at-the-money options
• Current stock price: USD 79
• Option analysis:
  • Option A (Call, Strike 75): In-the-money (current price 79 > strike 75)
  • Option B (Call, Strike 80): Near at-the-money (current price 79 ≈ strike 80)
  • Option C (Put, Strike 80): Near at-the-money (current price 79 ≈ strike 80)
  • Option D (Put, Strike 95): Deep in-the-money (current price 79 < strike 95)

Why Option D is best for delta-normal VaR:

• Option D is deep in-the-money, resulting in the lowest gamma among all positions
• Gamma is equal for call or put options with identical characteristics
• Lower gamma means less curvature risk, making the linear approximation of delta-normal VaR more accurate
• Options A, B, and C are closer to at-the-money and therefore have higher gamma, making delta-normal VaR less suitable

The delta-normal VaR will offer the best approximation of true risk for Option D due to its minimal curvature risk.