Vanna

Vanna is a second-order sensitivity of an option's price, one of the less familiar option Greeks. It measures the change in an option's delta for a change in implied volatility. The same number also gives the change in vega for a change in the price of the underlying asset. Mathematically it is the cross derivative $\partial^2 V / \partial S \, \partial \sigma$, where $V$ is the option value, $S$ the underlying price and $\sigma$ the volatility. Vanna is close to zero for at-the-money options and largest for options moderately out of the money.

Vanna matters because price and volatility tend to move together: in equity markets, volatility usually rises when prices fall. A trader hedging delta will find the hedge drifting as volatility shifts, even if the price is unchanged. Positions that are long one wing of the volatility skew and short the other carry substantial vanna. It is commonly monitored together with vomma, particularly in currency options.