Explanation

In derivatives pricing and risk management, risks are categorized into:

First-Order Risks:

• Delta: Measures the sensitivity of the option price to changes in the underlying asset price (first derivative with respect to price)
• Vega: Measures sensitivity to changes in volatility (first derivative with respect to volatility)
• Theta: Measures sensitivity to time decay (first derivative with respect to time)
• Rho: Measures sensitivity to interest rate changes (first derivative with respect to interest rates)

Second-Order Risks:

• Gamma: Measures the rate of change of delta with respect to changes in the underlying asset price (second derivative with respect to price)
• Vanna: Measures sensitivity of delta to changes in volatility
• Volga/Vomma: Measures sensitivity of vega to changes in volatility
• Charm: Measures sensitivity of delta to time decay

Why Gamma is a second-order risk:

• Gamma = ∂²V/∂S² (second partial derivative of option value with respect to underlying price)
• It measures the curvature or convexity of the option's price curve
• Gamma risk becomes important for large price movements and for delta-hedged portfolios

Why the other options are incorrect:

• Vega (A): First-order risk - sensitivity to volatility changes
• Delta (B): First-order risk - sensitivity to price changes

Gamma is the correct answer as it represents a second-order risk that captures non-linear effects in option pricing.