Vanna
How delta changes when implied volatility moves.
Vanna measures the sensitivity of an option's delta to changes in implied volatility (IV). Equivalently, it measures how an option's vega changes as the underlying stock price moves. If a call has a vanna of 0.03, a 1-point increase in IV will increase the call's delta by approximately 0.03. Vanna is a second-order Greek that links delta and vega.
Why It Matters
Vanna explains a phenomenon that puzzles many traders: why delta seems to shift after a volatility event, even if the stock price has not changed much. After an earnings announcement, IV often drops sharply (IV crush). Vanna tells you that this IV drop will change the deltas of your positions, altering your directional exposure in ways that delta alone does not predict.
Vanna is particularly important for portfolio managers and market makers who maintain delta-neutral positions. A large move in IV can shift their portfolio delta significantly, requiring rebalancing. For retail traders, understanding vanna helps explain why an option's behavior changes during volatility events and why positions sometimes move in unexpected directions.
How It Works
Vanna is the partial derivative of delta with respect to IV, or the partial derivative of vega with respect to the stock price. It captures the cross-effect between price movement and volatility.
How vanna behaves by moneyness:
- ATM options: Vanna is near zero. ATM delta stays at approximately 0.50 regardless of IV changes.
- OTM options: Vanna is positive for calls, negative for puts. When IV rises, OTM options gain delta (their probability of expiring ITM increases). When IV falls, OTM options lose delta.
- ITM options: Vanna is negative for calls, positive for puts. When IV rises, ITM deltas move away from 1.0 toward 0.50. When IV falls, ITM deltas move toward 1.0.
The intuition: Higher IV means more uncertainty about where the stock will end up. This uncertainty pushes all deltas toward 0.50 — OTM deltas increase and ITM deltas decrease. Lower IV does the opposite, pushing deltas toward their extremes (0 or 1.0).
Vanna flows and market impact: Dealer vanna hedging can create systematic market effects. When dealers are short options (common due to retail buying), a drop in IV reduces their delta hedges, potentially triggering stock selling. This is one mechanism by which volatility events feed back into price action.
Quick Example
You hold a 25-delta OTM call on stock MNO with vanna of 0.04. IV is currently 35%. A market event causes IV to spike from 35% to 45% — a 10-point jump. Vanna predicts your call's delta increases by approximately 0.04 x 10 = 0.40. Your 25-delta call now behaves more like a 65-delta call, dramatically increasing your directional exposure.
Conversely, after earnings, IV drops from 45% to 25% (a 20-point drop). That same call's delta decreases by roughly 0.04 x 20 = 0.80 — though in practice the effect is limited since delta cannot go below zero. The key point is that the IV drop reduces your option's directional sensitivity far more than the raw delta number suggested.