Vanna
Delta sensitivity to volatility changes
What is Vanna?
Vanna 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.
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.
Example
When IV drops, positive vanna positions see delta increase, forcing dealers to sell stock to re-hedge, creating downward pressure.
Related Terms
Frequently Asked Questions
What does vanna measure in options trading?
Vanna measures how an option's delta changes when implied volatility changes. It is a cross-Greek linking directional exposure and volatility exposure. Positive vanna means delta increases when IV rises and decreases when IV falls. It helps traders understand how their directional risk shifts in different volatility environments.
How does vanna affect market maker hedging?
When market makers hold large options positions, changes in IV alter their delta exposure through vanna. As IV drops, dealers with positive vanna see declining delta in their positions, forcing them to buy stock to re-hedge. As IV rises, they must sell stock. These hedging flows can create significant directional pressure in the market.
Which options have the highest vanna?
Out-of-the-money options have the highest absolute vanna because their delta is most sensitive to volatility changes. At-the-money options have near-zero vanna since their delta stays close to 0.50 regardless of IV. Deep in-the-money options also have low vanna as their delta is already near 1.0.
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