Vanna

Complete definition

Vanna is a second-order cross-Greek that measures the rate of change of an option's delta with respect to changes in implied volatility. Equivalently, it measures how an option's vega changes as the underlying price moves. Mathematically, vanna is the partial derivative of delta with respect to implied volatility, making it one of the most important cross-sensitivities in options risk management. How it works: Vanna captures the interaction between directional risk (delta) and volatility risk (vega). When implied volatility rises, options with positive vanna see their delta increase, meaning they become more directionally sensitive. Conversely, when IV falls, positive vanna positions lose delta. Out-of-the-money calls have positive vanna (delta increases as IV rises), while out-of-the-money puts have negative vanna. At-the-money options have near-zero vanna because their delta is already close to 0.50. For example, consider a portfolio of market makers who are short OTM calls on SPY with a collective positive vanna exposure. If the VIX drops from 18 to 14, the delta on those short calls decreases, meaning the dealers' short delta hedges become oversized. To rebalance, they must buy stock, creating upward price pressure. This is why volatility compression often accompanies rallies: dealer vanna hedging creates a positive feedback loop. Vanna is critical for understanding market structure flows. Aggregate dealer vanna exposure can explain why markets sometimes rally into low-volatility environments and sell off sharply when volatility spikes. Options analytics platforms that track net vanna exposure across all strikes and expirations provide valuable insight into potential dealer hedging pressure that can amplify or dampen market moves.