Sticky Delta
The regime where the curve travels with the market and the at-the-money never blinks.
Quick answer: Sticky delta is the volatility-surface regime — also called sticky moneyness — in which the entire smile slides sideways along with spot, so the at-the-money implied volatility stays unchanged while every individual strike's implied volatility moves as its distance from spot changes.
In simple words
Sticky delta is the mirror image of sticky strike. Instead of the curve staying nailed to strikes while spot walks along it, the whole curve travels with spot. Picture the downward-sloping NIFTY skew, and now imagine that when spot rises from 24,000 to 24,600, the entire curve picks up and slides 600 points to the right, keeping its shape and its position relative to spot exactly. The consequence is the opposite of sticky strike: the at-the-money volatility does not change at all, because the at-the-money point is always the same place on a curve that moves with it. What changes instead is every individual strike's volatility, because each strike is now a different distance from spot than it was before.
The name comes from the fact that implied volatility is sticky to moneyness — to a strike's position relative to spot — rather than to the strike itself. A 25-delta option keeps its volatility because it is always the same 25-delta distance out; the fixed 24,000 strike does not, because it used to be at the money and is now 600 points in the money. This is the regime you tend to see in trending markets, where the market carries its whole view of risk along with it as it moves. It is opposite bookkeeping to sticky strike, and — crucially — it puts the opposite sign on the delta correction.
The picture
The whole curve slid right with spot
The skew translates sideways as spot rises from 24,000 to 24,600.
Professional explanation
What 'sticky delta' actually asserts
Sticky delta, or sticky moneyness, is a claim about dynamics: as spot moves, the implied-volatility curve translates with it, so that an option's volatility depends only on its moneyness — its position relative to spot — and not on its absolute strike. The 25-delta put keeps its volatility through the move because it remains the 25-delta put; the at-the-money option keeps its volatility because it remains at the money. What does not keep its volatility is any fixed strike, because a strike that was at the money before the move is now in the money and therefore sits at a different point on the translated curve. The visible signature of the regime is a constant at-the-money volatility: on the reference chart, spot rises 600 points and the at-the-money print stays at about 12.8%, while the old 24,000 strike, now 600 points in the money, moves up the skew to a higher volatility. Sticky delta thus builds in no relationship between spot and at-the-money volatility — a very different assumption from sticky strike's built-in negative one.
Why trending markets tend to print it
Sticky delta is the natural regime when the market is trending and carries its entire view of risk along with the level. In a sustained move, traders do not think the risk landscape is fixed in strike space — they think of risk in relative terms, as "how far out of the money", and as spot grinds higher or lower they simply drag the whole smile with it. The crash strike is always "about ten percent below spot", wherever spot happens to be, rather than a specific frozen number. This is why sticky delta and sticky strike sort so naturally into trending versus range-bound markets: a range-bound market has fixed reference strikes it keeps returning to, so its curve stays put; a trending market has no fixed reference, so its curve travels. The regime is therefore not an arbitrary modelling choice but a description of how the market is thinking about risk — in absolute strikes or in relative moneyness — and that mode of thought changes with the market's character.
The opposite sign on the delta correction
This is where sticky delta bites, and the bite is the reverse of sticky strike's. The true delta is again Δ_adj = Δ_BS + ν·(∂σ/∂S), and the regime is the assumption about ∂σ/∂S. Under sticky delta the curve slides with spot, so a fixed strike's volatility does change as spot moves — and on a downward equity skew it changes in a specific direction. When spot rises, a fixed strike that was at the money becomes in the money, moving up the put side of the translated skew toward higher volatility, so ∂σ/∂S is positive for that strike. A positive ∂σ/∂S makes the correction term positive, so the true delta of a call sits above its Black–Scholes delta — the exact opposite of the zero correction sticky strike gave and, further still, the opposite direction from the sticky-local-volatility regime, where the true delta sits below Black–Scholes. This is why confusing the regimes is so costly: it is not a matter of sizing a correction slightly wrong, it is applying it with the wrong sign. A delta corrected in the wrong direction leaves you more exposed than the uncorrected Black–Scholes delta would have, because you have deliberately walked away from the right answer.
Sticky delta implies a specific skew dynamic, and markets sit in between
There is a subtle argument worth making explicit: pure sticky delta is not fully self-consistent as a model of how volatility should behave. If the smile translates rigidly with spot, then the risk-neutral dynamics it implies can be shown to require the skew to behave in a very particular way that clashes with no-arbitrage under some conditions — which is why sticky delta, like sticky strike, is best treated as a useful local approximation rather than a complete model. More important is the empirical finding, which a model brochure would prefer to leave out: index option markets do not sit at either pole. They behave as something between sticky strike and sticky delta, and often closer to the sticky-local-volatility regime in which the smile moves down more than one-for-one as spot rises, giving a true delta below Black–Scholes. So the two regimes on these pages are not a menu to pick from but the endpoints of a spectrum the market moves along — calmer and range-bound toward sticky strike, trending toward sticky delta, stressed toward sticky local volatility — and the honest practitioner estimates where on that spectrum the market currently sits rather than committing to a corner. The market switches regime without announcing it, and a book that assumes a fixed regime is quietly wrong most of the time.
Why the regime decides whether a hedge is a hedge
A discretely re-hedged delta position against the true continuous delta.
Formula
The delta the regime forces on you
Δ_adj = Δ_BS + ν · (∂σ/∂S)
The true, minimum-variance delta is the Black–Scholes delta plus vega times how fast the option's own implied volatility moves as spot moves. Under sticky delta the curve translates with spot, so a fixed strike's volatility does change: for an equity skew, a strike that becomes more in-the-money as spot rises moves up the curve, making ∂σ/∂S positive and the correction positive, so the true delta sits ABOVE the Black–Scholes delta. This is the opposite sign to the sticky-strike result (correction zero) and to the sticky-local-volatility result (correction negative), which is exactly why choosing the wrong regime corrects the delta the wrong way.
- Δ_adjThe regime-adjusted (minimum-variance) delta — the hedge ratio that actually minimises the variance of the hedged position.
- Δ_BSThe Black–Scholes delta computed at the option's own implied volatility, before any regime correction.
- νVega — the option's sensitivity to a change in implied volatility, per one percentage point, per unit of the underlying.
- ∂σ/∂SThe rate at which the option's implied volatility changes as spot moves. Sticky delta makes this non-zero, and positive for a fixed strike on a downward equity skew.
- SSpot price of the underlying — 24,000 for NIFTY here, rising to 24,600 in the worked example.
Sticky delta as a rule for the smile
σ(K, S) = g(K / S), so ∂σ_ATM/∂S = 0
Under sticky delta, implied volatility is a fixed function of moneyness K/S rather than of the strike alone, so the whole curve translates with spot. The at-the-money volatility — always at moneyness 1 — is therefore constant, which is the regime's visible signature: spot rises 600 points and the at-the-money print stays put at about 12.8%. A fixed strike's volatility, by contrast, changes because its moneyness changes as spot moves.
How to hedge under a sticky-delta assumption
- Confirm the market is trending and carrying its view of risk with it — sticky delta is the trending-market regime, and a poor fit for a range-bound one.
- Track implied volatility by moneyness, not by strike: hold the curve fixed relative to spot and let it translate as spot moves.
- Expect the at-the-money volatility to stay roughly constant through a move; if it is falling as spot rises, you are drifting toward sticky strike or sticky local volatility, not sticky delta.
- For each fixed strike, recognise its volatility will change as spot moves because its moneyness changes — a strike becoming more in-the-money on a downward skew moves up the curve.
- Apply the delta correction with the sticky-delta sign: Δ_adj = Δ_BS + ν·(∂σ/∂S) with ∂σ/∂S positive for a fixed strike, so the true delta sits above the Black–Scholes delta.
- Do not blindly commit to the corner. Estimate where between sticky strike, sticky delta and sticky local volatility the market actually sits, because index markets usually sit between the poles.
- Re-check the regime after each large move and whenever the market changes character, because the market switches regime without announcing it.
Practical example
NIFTY worked example
NIFTY is at 24,000 with the at-the-money strike printing about 12.8% and the 24,000 strike, being at the money, printing the same. Spot rises to 24,600. Under sticky delta the whole curve slides 600 points to the right, so the new at-the-money strike — 24,600 — also prints about 12.8%: the at-the-money volatility is unchanged, which is the regime's signature. But your original 24,000 strike is now 600 points in the money, sitting on the put side of the translated curve, and it moves up to a higher volatility — on the reference numbers, from about 12.8% to roughly 14.5%. Interpret the hedging consequence. If you are short that 24,000 call, its own volatility has risen with the move, and the correct delta must add a positive correction: Δ_adj = Δ_BS + ν·(∂σ/∂S) with ∂σ/∂S positive, so your true delta is above the Black–Scholes delta. Under sticky strike the same option's volatility would have been unchanged and the correction zero. Same option, same 600-point move, opposite hedging instruction — which is the entire reason the regime you assume is not a technicality.
BANKNIFTY worked example
BANKNIFTY in a strong directional run illustrates the constant at-the-money signature. Suppose BANKNIFTY is trending up hard from 52,000 and the market is dragging its whole risk view along, behaving as sticky delta. At 52,000 the at-the-money strike prints about 15.5%. Spot runs to 52,600; under sticky delta the new at-the-money 52,600 strike still prints about 15.5% — the at-the-money volatility has not moved, even though the index has. Meanwhile the old 52,000 strike, now 600 points in the money, has slid up the curve to a higher volatility. The lesson that differs from the NIFTY one is about what a constant at-the-money print does and does not tell you: a trader watching only the at-the-money number would see BANKNIFTY volatility "unchanged" and might conclude nothing is happening in the options market. Plenty is happening — every individual strike has repriced — it just cancels out exactly at the money. A flat at-the-money volatility in a trending market is a signature of sticky delta, not a sign of a quiet options market.
Lot sizes used above (NIFTY 75, BANKNIFTY 30) are those in force at the time of writing; NSE revises them periodically. Figures exclude brokerage, STT, exchange charges, stamp duty and GST. Examples are teaching scenarios built on round numbers — they are not historical quotes, not backtests and not trade calls.
Advantages & limitations
What it is good for
- It matches how a trending market genuinely thinks about risk — in relative moneyness rather than fixed strikes — so it is the right description precisely when the market is moving with conviction.
- It gives a clean, memorable signature: a constant at-the-money volatility through a move, which is easy to check against the screen and immediately distinguishes it from sticky strike.
- It supplies the correct opposite-signed delta correction for a trending regime, so a book hedged with sticky-delta awareness carries less unintended directional risk when the market is actually translating its curve.
- It keeps fixed-delta measures like the 25-delta risk reversal stable through a move, which is why quoting the skew in delta terms is robust under exactly this regime.
- It clarifies, by contrast with sticky strike, that the regime — not the shape of the smile — is what determines the hedge, forcing a trader to think about dynamics rather than snapshots.
Where it breaks down
- It fails in range-bound markets, where the curve stays fixed to strikes rather than translating, so its constant-at-the-money assumption is simply the wrong description of the dynamics.
- Pure sticky delta is not fully self-consistent as a model: a rigidly translating smile implies skew dynamics that can clash with no-arbitrage, so it is only a local approximation.
- Its positive delta correction is the wrong sign whenever the market is actually in the sticky-local-volatility regime, where the true delta sits below Black–Scholes — so a wrong regime call is worse than no correction.
- Index markets rarely sit exactly at the sticky-delta pole; they lie somewhere on a spectrum and drift along it, so committing to the corner is usually at least partly wrong.
- It says nothing about the level of volatility, only about how the curve translates, so it cannot warn you that the whole surface is about to lift or collapse.
Common mistakes
- Applying the sticky-delta positive delta correction in a market that is actually range-bound or stressed. The sign is wrong for those regimes, and a wrong-sign correction leaves you more exposed than the uncorrected Black–Scholes delta.
- Reading a constant at-the-money volatility in a trending market as "nothing is happening" in options. Under sticky delta every individual strike has repriced; the changes merely cancel at the money, which is a signature of the regime, not a quiet market.
- Assuming a fixed strike keeps its volatility under sticky delta. It does not — only fixed-moneyness options do — so a strike that becomes more in-the-money slides up the curve, and treating its volatility as constant misprices it.
- Hard-coding sticky delta as a permanent regime. Index markets sit between the poles and switch without warning, so a book that always assumes sticky delta is systematically mis-hedged for long stretches.
- Confusing sticky delta with sticky strike. They put opposite instructions on the same option after the same move, so swapping them flips the sign of the delta correction — the single most consequential error in this section.
- Treating pure sticky delta as a complete, arbitrage-consistent model. It is a local approximation whose rigidly translating smile can clash with no-arbitrage, so building an exotic book on it unquestioned invites hidden model risk.
Professional usage
Desks lean on the sticky-delta assumption when the market is trending and think naturally in delta or moneyness terms, quoting and risk-managing the skew as a fixed-delta object — the 25-delta risk reversal, the 10-delta wings — precisely because those quantities are stable when the curve translates with spot. Under this regime a desk applies the positive-signed skew-delta correction to its spot hedges and expects the at-the-money volatility to hold roughly constant through a move, using any deviation from that as evidence the regime is shifting. Just as with sticky strike, the assumption doubles as a diagnostic: the observed behaviour of at-the-money volatility as spot moves tells the desk whether it is nearer the sticky-delta pole, the sticky-strike pole, or the sticky-local-volatility regime beyond, and therefore which sign and size of correction its delta actually needs.
Quantitative and risk teams treat the position on the sticky-strike-to-sticky-local-volatility spectrum as a first-order model-risk axis. Because the delta corrections at the two ends have opposite signs, a book's aggregate directional exposure can flip depending on the regime assumed, so risk stresses the portfolio across the whole spectrum and sizes the worst case rather than trusting a single point estimate. Volatility arbitrage desks are especially attentive, because a persistent regime misassumption produces a small, systematic, one-directional hedging error — a slow leak in the hedged profit and loss that is invisible in any single day's marks and only becomes obvious as a trend over months. The uncomfortable operational reality is that the market changes regime without notice, so the estimate is never finished.
Key takeaways
- Sticky delta, or sticky moneyness, is the regime in which the whole smile slides sideways with spot, so at-the-money implied volatility stays constant while every individual strike's volatility changes.
- It typifies trending markets, which carry their entire view of risk along with the level and think of risk in relative moneyness rather than fixed strikes.
- Its delta correction has the opposite sign to sticky strike's: with ∂σ/∂S positive for a fixed strike on an equity skew, the true delta sits above the Black–Scholes delta.
- Because sticky delta, sticky strike and sticky local volatility give corrections of different signs, confusing the regimes flips the sign of your hedge — worse than applying no correction at all.
- Index markets sit between the poles rather than at either one and switch regime without announcing it, so the honest task is estimating where on the spectrum the market currently is, not committing to a corner.
Sticky delta is the trending-market twin of sticky strike: the curve travels with spot, the at-the-money volatility never blinks, and every fixed strike reprices as its moneyness changes. Its one indispensable lesson is the sign of the delta correction — positive here, zero under sticky strike, negative under sticky local volatility — because getting that sign wrong hedges you in the wrong direction, which is worse than not hedging the skew at all. And the honest, unmarketable truth is that no real index sits at either pole: the market slides along the spectrum between them and switches without warning, so the regime is never a setting you lock in, only a hypothesis you keep testing against the market's own movement.
Frequently asked questions
What is sticky delta in simple terms?
Why does at-the-money volatility stay constant under sticky delta?
Why is it called sticky delta or sticky moneyness?
What kind of market prints sticky delta?
How is sticky delta different from sticky strike?
What does sticky delta do to my delta?
Why is the delta correction the opposite sign to sticky strike?
What happens if I confuse sticky delta with sticky strike?
Is pure sticky delta a complete model?
Where do real index markets sit — sticky strike or sticky delta?
What does a constant at-the-money volatility in a trend tell me?
Does a fixed strike keep its volatility under sticky delta?
Why does sticky delta keep the 25-delta risk reversal stable?
What is the sticky-local-volatility regime?
How do I know which regime the market is in?
Is sticky delta better than sticky strike for hedging?
Does sticky delta tell me the level of volatility is rising?
Why is a wrong-sign delta correction worse than none?
How often does the market change regime?
What is the single most important thing to remember about sticky delta?
Voice search & related questions
Natural-language questions people ask about sticky delta.
What does sticky delta mean?
Why doesn't at-the-money volatility change when the market moves under sticky delta?
How does sticky delta change my hedge versus sticky strike?
When should I assume sticky delta?
Is the market ever purely sticky delta?
What does it mean if at-the-money volatility stays flat while the market trends?
Why is confusing the regimes so dangerous?
Sources & references
- Emanuel Derman — Regimes of Volatility (Goldman Sachs, 1999)
- Lorenzo Bergomi — Stochastic Volatility Modeling (skew dynamics and regimes)
- Hagan, Kumar, Lesniewski & Woodward — Managing Smile Risk (SABR, 2002)
- NSE — NIFTY and BANKNIFTY option chains
Last reviewed 10 July 2026. Educational content only — not investment advice.