Explanation

Correct Answer: A

The delta-normal model used by Bank A provides only a linear approximation of the option's price sensitivity, while the Monte Carlo simulation used by Bank B performs full revaluation that captures the non-linear characteristics of the option.

Key Points:

1. Convexity of Option Price Function: The price of a call option is convex with respect to the underlying stock price. This means that for large price movements, the actual option price change is greater than what the linear delta approximation would suggest.

2. Delta-Normal Model Limitations:

   • Uses only the delta (first derivative) for risk measurement
   • Assumes linear relationship between option price and underlying price
   • Does not capture gamma (second derivative) effects
   • Overstates downside risk for long option positions

3. Monte Carlo Full Revaluation:

   • Recalculates the option price for each simulated scenario
   • Captures the full non-linear payoff structure
   • Accounts for convexity effects
   • Provides more accurate risk measurement

4. VaR Impact: For a long call option position, the convexity provides protection against large losses, which the delta-normal model fails to capture. Therefore, Bank A using delta-normal will estimate higher VaR than Bank B using full revaluation.

This demonstrates the importance of using appropriate risk measurement methodologies for non-linear financial instruments like options.