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Vanna

How delta changes when implied volatility changes — equivalently, how vega changes when price moves. The link between the skew and directional exposure.

Vanna explains why a position that looks delta neutral can become directional after a volatility shift. Raise implied-volatility and out-of-the-money options gain delta, because a wider distribution makes reaching the strike more plausible.

It matters most for skewed books. A trader short out-of-the-money puts is short vanna: when the market falls, volatility rises, and their put deltas grow faster than the price move alone would suggest. Losses arrive from two directions at once.

Example: you are short the XYZ $45 put at 0.18 delta with implied-volatility at 25%. A sharp drop takes IV to 35% while XYZ falls only to $49. Delta is now 0.24 despite the small move — vanna added exposure you never chose.

Related: second-order-greeks, charm, volatility-skew, vomma

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

How a call option's delta changes with the underlying priceAn S-shaped curve rising from zero, passing through about a half at the strike, and flattening near one.Delta of a call option1.000.5008090110120Out of the moneyAt the moneyIn the money1.00 means it moves one-for-one with the stockdelta ≈ 0.50 at the strikeStrike 100Underlying price
Delta across the range of prices. Delta says how much a call's price moves for a one-point move in the stock. Far below the strike it is near 0 and the option barely reacts; at the strike it is about 0.50; far above it approaches 1 and tracks the stock.

Educational only, not advice. Spotted an error? Post in Site Feedback.