Vanna and Volga
Vanna and Volga are second-order Greeks used to manage the risk associated with changes in the volatility surface. Vanna measures the sensitivity of an option's Delta to changes in implied volatility, or equivalently, the sensitivity of Vega to changes in the underlying price.
Volga measures the sensitivity of an option's Vega to changes in its own implied volatility, essentially the "volatility of volatility." These metrics are crucial for traders who manage complex portfolios where simple Delta and Vega hedging are insufficient. By managing Vanna and Volga, traders can better hedge against scenarios where price moves and volatility changes are correlated.
They are essential tools for precision risk management in sophisticated derivatives books.