Second-Order Risk

Second-order risk refers to risks that arise from the rate of change of primary risk factors, such as gamma or vanna. While primary risks like delta or vega describe the impact of a direct change in price or volatility, second-order risks describe how those sensitivities themselves evolve.

For example, gamma measures how delta changes as the underlying price moves, which is crucial for managing the stability of a hedge. In complex derivative structures, failing to account for second-order risks can lead to unexpected losses during volatile periods.

Professional risk managers use advanced models to monitor these sensitivities, ensuring that the portfolio remains robust even when market conditions shift rapidly. It is the difference between simple linear risk and the nuanced, non-linear reality of derivative pricing.