Vanna
The cross-Greek that links your delta to volatility and your vega to price.
Definition
Vanna is a second-order Greek that measures how an option's delta changes when implied volatility moves. By symmetry, it equally describes how vega changes when the underlying price moves. In short, vanna is the bridge between an option's price sensitivity and its volatility sensitivity.
Formula
Vanna is the mixed partial derivative of the option value with respect to spot price and volatility: Vanna = ∂Delta / ∂σ = ∂Vega / ∂S. It is largest for out-of-the-money options and tends toward zero deep in or deep out of the money.
Why it matters
Vanna explains why your delta hedge drifts when volatility shifts even if price has barely moved. For desks running large books, vanna exposure can drive hedging flows that feed back into the underlying, particularly around volatile sessions and expiry. Ignoring it can leave a position quietly mis-hedged.
Example
You hold an out-of-the-money call with delta 0.30. Implied volatility jumps, and the call's delta climbs toward 0.38 even though spot is unchanged. That move in delta caused purely by the volatility change is vanna at work, and it would force you to adjust your hedge.
See it live
Watch how delta and vega shift together across strikes on TradePulse's live option chain.