Vanna is a second-order option Greek: the rate at which delta changes for a one-point change in implied volatility. By symmetry it is also the rate at which vega changes for a one-point move in the underlying. It is largest for out-of-the-money and in-the-money options and close to zero at the money, where delta is insensitive to volatility.

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Second-Order Greeks

Vanna

Q: What is the sign of vanna for calls and puts?

A long out-of-the-money call has positive vanna: higher implied volatility raises its delta, because a bigger expected move makes finishing in the money more likely. A long out-of-the-money put has negative vanna in the usual convention: its delta becomes more negative as volatility rises. In-the-money options have the opposite signs, since higher volatility pulls their delta back toward 0.5.

Q: Why does vanna matter to a trader?

Because a position hedged to zero delta at one implied volatility is no longer delta-neutral when volatility changes. On an index, volatility tends to rise when prices fall, so vanna links the two: a falling market raises IV, which changes the deltas of every out-of-the-money position, which forces hedging. A book with large vanna picks up or sheds directional exposure without the underlying having to move through its strikes.

Q: What is dealer vanna hedging?

Market makers who are net short out-of-the-money puts carry vanna exposure. When implied volatility falls in a calm, rising market, the deltas of the puts they are short shrink, leaving them over-hedged short futures, so they buy back, which supports the index. When volatility rises in a fall, the same puts gain delta and dealers sell futures, adding to the decline. This feedback is one explanation for the grind higher in low-volatility periods and the acceleration in sell-offs.

Q: How is vanna different from gamma and vega?

Gamma is how delta changes when the underlying moves; vega is how price changes when volatility moves; vanna is the cross term, how delta changes when volatility moves. Gamma is largest at the money, vanna away from it. A position can be gamma-neutral and still carry vanna, which is why it is tracked separately on books with many out-of-the-money strikes.

Delta tells you your exposure at today's volatility. Vanna tells you how that exposure changes when volatility moves, which on an index means when the market falls.

In short: vanna is the change in an option's delta for a one-point change in implied volatility; equivalently, the change in vega for a one-point move in the underlying. It is near zero at the money and largest for out-of-the-money and in-the-money strikes. A long out-of-the-money call has positive vanna (delta rises with IV); a long out-of-the-money put's delta becomes more negative as IV rises. Because index volatility rises when prices fall, vanna couples volatility to direction and drives a well-known hedging feedback among option dealers.

The intuition

Delta is the probability-weighted chance of finishing in the money, roughly. For an out-of-the-money call that chance depends on how far the underlying can plausibly travel, and that is what implied volatility describes. Raise IV and the 24,500 call, 500 points above spot, becomes more reachable; its delta rises. Lower IV and it drifts toward irrelevance; its delta falls. At the money the option is a coin toss at any volatility, so its delta hardly responds. Vanna is the size of this response.

The same number read the other way is how vega responds to the spot. An out-of-the-money call's vega grows as the underlying rises toward its strike and shrinks as it falls away. Vanna being a cross-derivative means both readings are the same quantity, and either is a reason to care about it.

Formula and worked example (illustrative numbers)

In the Black-Scholes model, vanna = −N′(d₁) × d₂ / σ, where N′ is the standard normal density. Scaled to a one-point change in IV, it is that quantity divided by 100. Suppose NIFTY is at 24,000 with 27 days to expiry and implied volatility at 14%:

Call strike	Premium	Delta at 14%	Vanna (per IV point)	Delta if IV rises to 17%
23,000 (ITM)	₹1,156	0.90	−0.016	about 0.85
23,500 (ITM)	₹746	0.76	−0.015	about 0.72
24,000 (ATM)	₹424	0.56	−0.003	about 0.55
24,500 (OTM)	₹207	0.35	+0.011	0.38
25,000 (OTM)	₹86	0.18	+0.018	about 0.23

A three-point rise in IV with the index unchanged lifts the 24,500 call's delta from 0.35 to 0.38. On ten lots (650 units) that is 20 units of extra delta, with nothing having happened to the spot. A trader who had sold those calls and hedged with futures is now under-hedged by that amount and must buy. The in-the-money calls move the other way: higher volatility pulls their deltas back toward 0.5, which is the mirror of the same effect.

For puts the sign flips in the usual convention because put delta is negative: a long 23,000 put's delta goes from about −0.10 toward −0.15 as IV rises from 14% to 17%. Its vanna is reported as negative, and a short put position therefore has positive vanna.

Vanna across strikes for a long call. It is zero near the money and changes sign there; out-of-the-money strikes carry the most.

Why it matters to an options trader

Delta hedges drift with volatility. A position delta-neutral at 14% IV is directional at 17%. Short out-of-the-money puts, the most common retail position on NIFTY, pick up short delta exactly when the market falls and IV rises.
It explains the "it moved against me without moving" complaint. A sold strangle can lose on a day the index closes flat if IV rose, through vega directly and through vanna shifting the hedge.
It links the skew to direction. The put skew exists because IV and spot move inversely; vanna is the Greek that prices that relationship into a hedge.
Dealer vanna flows move the index. When dealers are short puts and IV drifts down in a calm market, their hedges unwind into buying; when IV spikes, the same hedges turn into selling. The pattern of slow rises and fast falls has vanna hedging in it.

Common mistakes

Hedging delta once and assuming it holds. On a book of out-of-the-money options the delta changes with IV every session, whether or not the spot moves.
Ignoring vanna on expiry day. Near expiry vanna is concentrated at strikes just out of the money; a small IV change there shifts deltas sharply and adds to the pinning and breaking behaviour of the final hour.
Confusing vanna with gamma. Both change delta, but gamma needs the spot to move and vanna needs IV to move. A sell-off delivers both at once, which is why short-put books lose faster than their delta and gamma alone suggest.
Treating vanna as a retail-irrelevant Greek. Any trader short out-of-the-money options on NIFTY or Bank Nifty carries it, usually in the direction that hurts in a fall.
Reading the sign without the position. Long call vanna is positive out of the money; the same call sold is negative; a long put out of the money is negative, sold is positive. Always state long or short.

Indian-market specifics

Retail positioning on NIFTY and Bank Nifty is heavily short out-of-the-money options, so the aggregate retail book is short vanna on the put side; a rise in India VIX during a fall adds short delta to those books collectively.
On the Tuesday weekly, vanna is concentrated within a few hundred points of spot on the final two sessions; the monthly spreads it across a wider band of strikes.
NSE's option chain does not publish vanna; it is computed from the Black-Scholes inputs by platforms and brokers that show second-order Greeks, using the chain's own implied volatility per strike.
Bank Nifty's higher volatility and 100-point strike spacing give it larger vanna per strike than NIFTY at equivalent moneyness.

FAQ

What is vanna?

The change in delta per one-point change in implied volatility, equivalently the change in vega per point of spot.

What is the sign of vanna for calls and puts?

Positive for long out-of-the-money calls, negative for long out-of-the-money puts, reversed in the money and reversed again when sold.

Why does vanna matter to a trader?

Because a delta hedge set at one IV drifts when IV changes, and on an index IV changes when the market falls.

What is dealer vanna hedging?

The buying and selling of futures that market makers do as IV changes shift the deltas of the options they hold, which feeds back into the index.

How is vanna different from gamma and vega?

Gamma is delta against spot, vega is price against IV, vanna is delta against IV: the cross term.

Delta and IV, strike by strike

The NIFTY option-chain page shows the implied volatility and open interest at each strike from the latest close, which is where the vanna in the market sits. In the app, the option chain shows the Greeks at every strike for the selected expiry.

NIFTY option chain How the Greeks interact

Related terms

Vomma, the other second-order volatility Greek
Delta Hedging, the practice vanna complicates
Volatility Skew, the market's pricing of the spot-IV link
Second-Order Greeks, the full family