Vanna

Vanna is a second-order Greek. It measures how much an option's delta changes when implied volatility changes. Put another way, it also shows how vega changes when the stock price moves.

"Second-order" means it describes a change in another Greek rather than a change in the option's price directly.

Take an out-of-the-money call with a delta of 0.30. If implied volatility rises, the market is pricing in bigger moves, so the chance of the call finishing in the money goes up and its delta rises, say to 0.35. The amount delta shifts for each point of volatility is what vanna measures.

For a deep in-the-money call the effect usually goes the other way, so the sign of vanna depends on where the strike sits. The numbers here are illustrative.

Market makers who sell options usually hedge their delta by trading the stock or futures. When implied volatility changes, the deltas of their options change too, so they have to adjust their hedges. That trading is sometimes called vanna flow.

Some traders try to use it to guess market direction, but the effect depends on how dealers are positioned, which cannot be seen directly. Estimates vary, so vanna is not a reliable signal by itself.