Friday 12 Jun 2026. Nifty rose 1.99 percent and the 30 day at the money implied volatility fell 1.12 points. On Thursday 19 Mar 2026 Nifty fell 3.26 percent and the same measure rose 4.40 points. Desks call it the smile moving with the index, and the rule they assume for how it moves decides the hedge. Three rules are common: sticky strike, sticky delta and local volatility. This module sets them side by side, measures the skew that two of them need, and checks all three against the six largest falls and six largest rises of Nifty in an NSE file of 300 sessions. None of the three fits those days. That is the finding. Every figure comes from NSE end of day files, dated, so nothing here is live and nothing is a view on the next move.
3By the end you can
- Say what sticky strike, sticky delta and local volatility each predict for the at the money volatility.
- Measure a skew slope from a dated chain and turn each rule into a hedge ratio.
- Say why two dates cannot settle a regime, and what twelve big days showed.
The idea, plainly
What does sticky mean?
When the index moves, every implied volatility on the chain can move. A rule says how. Take two things off the chain: the at the money volatility, and the skew, which is the slope of the smile in volatility points for each one percent move of the strike. The skew is negative for Nifty, as the skew measures module shows.
- Sticky strike. The volatility at each strike stays where it was. When the index rises, the at the money point slides to a higher strike, so the at the money volatility changes by the skew slope.
- Sticky delta. The whole smile slides with the index, which is close to saying it is fixed in moneyness. The at the money volatility does not change.
- Local volatility. The smile moves the opposite way to the index. The at the money volatility changes by about twice the skew slope.
Three rules, three answers for the at the money vol
The maths: the skew stickiness ratio
Write R for the ratio of two slopes at the money: how the at the money volatility changes with the log of the index, over how the smile changes with the log of the strike.
R = (d vol_ATM / d ln S)
/ (d vol / d ln K at ATM)
For a smile that falls in strike, sticky delta gives R of zero, sticky strike gives one and local volatility about two, to first order. R is a way to measure a regime without adopting a model. A stochastic volatility model gives an R that depends on its parameters, so the class of model does not decide it.
For one option at a fixed strike the volatility changes by R minus one skew slopes, because the at the money point itself slides along the smile as the index moves. That is zero for sticky strike, where each strike keeps its own volatility.
Where does the screen delta come from?
An option chain shows a delta beside each strike. It is the Black 76 delta computed with that strike's own implied volatility held fixed. That is the sticky strike rule exactly: the volatility of the strike does not respond to the index, so no vega term enters the hedge. Under the other rules the option's own volatility moves with the index, and a vega term does enter. The number is not wrong. It answers one question, the one sticky strike asks.
Why does it matter?
Because the hedge ratio depends on it. The delta on a screen holds volatility fixed. If volatility moves with the index, the hedge that leaves the least variance is the delta plus the vega times the expected change of the option's own volatility for each point of index.
The maths: the minimum variance delta
Delta_mv = Delta
+ vega x (d vol_K / d S)
Here vol_K is the volatility of the option itself. With vega in rupees for one volatility point, and d vol over d S in points of volatility for one point of index, the second term is in the same units as delta. Put d vol over d S equal to R minus one, times the skew slope, divided by one percent of the forward, and each rule gives its own hedge ratio: above the screen delta for sticky delta, equal to it for sticky strike and below it for local volatility.
Read one more paragraph, 49 words
Take the 23,200 call of the 30 Jun expiry on 10 Jun 2026. Its implied volatility was 15.14 percent, its delta 0.525, its vega 21.6 rupees a unit for one volatility point, and the forward 23,240.10. The next sections turn each rule into a delta for it.
What do the models say?
Local volatility, which fits the whole surface at one moment, fixes R near two. A well known study of market smiles found that real markets did not behave that way, and that hedges derived from the model could be unstable and could do worse than plain Black hedges. Stochastic volatility models can give other values, depending on the correlation of the index with its variance and on how fast variance reverts. None of these decides the matter. The data do, and only for the window they cover.
Read one more paragraph, 81 words
Why two? In a local volatility model the implied skew is about half the slope of the local volatility itself, and the at the money implied volatility follows the local volatility at the index. Move the index by one percent and the local volatility changes by its own slope, which is twice the implied skew. A stochastic volatility model gets its moves from another place: the correlation between the index and its variance, which makes volatility fall when the index rises.
Worked example: 10 Jun to 16 Jun 2026
What did the at the money volatility do?
The skew first. On 10 Jun 2026 the 22,550 put, three percent below the forward, priced 16.13 percent and the 23,950 call three percent above it 14.34. The log distance between the strikes was 0.0602, so the slope was −0.30 vol points for each one percent move of the strike. Then the move: the forward rose from 23,240.10 to 24,001.00, up 3.27 percent, and the at the money volatility of the same expiry went from 15.03 to 12.11 percent.
| Points | 10 to 16 Jun | 1 to 2 Feb |
|---|---|---|
| Days left | 20 to 14 | 23 to 22 |
| Skew slope | −0.30 | −0.35 |
| Forward, % | 3.27 | 1.16 |
| Sticky delta | zero | zero |
| Sticky strike | −0.97 | −0.40 |
| Local vol | −1.95 | −0.80 |
| Observed | −2.92 | −1.90 |
Read 3 more paragraphs, 168 words
The same exercise runs from Budget Day, Sunday 1 Feb 2026, to the next session, for the 24 Feb expiry. The skew, from wings a log distance of 0.0604 apart, was −0.35 per one percent. The forward rose from 24,853.50 to 25,141.80, up 1.16 percent and the at the money volatility fell from 15.04 to 13.14.
In the table, the skew slope is in vol points for one percent of strike, the forward move is in percent, and the last three rows are changes of the at the money volatility in points.
In both pairs the at the money volatility moved by more than any rule predicted: −2.92 points against −1.95 at most in June, and −1.90 against −0.80 in February. Neither pair can tell the rules apart. In June four sessions and six days of time passed, and in February the Budget event left the chain, so part of the fall was event variance going out. Two dates cannot settle a regime. Many days can.
2 terms this section turns on
What do the largest days say?
Take the six largest one day falls and the six largest one day rises of Nifty in the file, and set the change of the 30 day at the money volatility beside each. The file covers 300 sessions from 1 Jul 2025 to 15 Sep 2026.
| Day | Move, % | ATM vol, pts |
|---|---|---|
| 19 Mar 2026 | −3.26 | 4.40 |
| 23 Mar 2026 | −2.60 | 6.46 |
| 30 Mar 2026 | −2.14 | 1.76 |
| 8 Jul 2026 | −2.12 | 2.92 |
| 27 Mar 2026 | −2.09 | 4.12 |
| 13 Mar 2026 | −2.06 | 2.01 |
| 8 Apr 2026 | 3.78 | −6.17 |
| 3 Feb 2026 | 2.55 | −1.22 |
| 12 Jun 2026 | 1.99 | −1.12 |
| 24 Mar 2026 | 1.78 | −4.11 |
| 25 Mar 2026 | 1.72 | −1.24 |
| 15 Apr 2026 | 1.63 | −2.20 |
On all twelve big days the volatility moved against the index
The big days moved the volatility further than any rule
Read one more paragraph, 147 words
On all twelve days the volatility moved against the index. A line through the origin fitted to the twelve has a slope of −1.39 vol points for each one percent move of the index. Against the skew slope of −0.30, that makes R about 4.7. It is above sticky strike, above local volatility and a long way above sticky delta. Day by day the response varied by a factor of several, so twelve points give a loose estimate. Read it as what it is: on the big days the index and its own volatility moved together far more than a fixed smile shape explains. Twelve extreme days from one file, mostly from the stress of March and April 2026, are not typical. On all the other days the slope was smaller. R is a descriptive number for a window, not a constant of the market.
How much does the skew slope itself move?
R is a ratio, so a slope that moves makes R move. The same recipe, the put and the call about three percent either side of the forward, gives these slopes, in vol points for each one percent move of the strike, on five dates.
| Date, expiry | Slope |
|---|---|
| 10 Jun 2026, 30 Jun | −0.30 |
| 16 Jun 2026, 30 Jun | −0.23 |
| 1 Feb 2026, 24 Feb | −0.35 |
| 2 Feb 2026, 24 Feb | −0.44 |
| 11 Jun 2025, 26 Jun | −0.39 |
Read 2 more paragraphs, 150 words
Divide the twelve day slope by each and R ranges from 3.2 to 6.0. It stays above two whichever date I pick. A slope between two points three percent apart also hides curvature. On 10 Jun 2026 the 23,950 call priced 14.34 percent and the 25,000 call 16.16, so the right side of the smile turns up. One slope at the money does not describe that, which is what the surface models of the previous module are for.
The 30 day measure is a constant maturity interpolation between expiries. As a day passes, weight moves from one expiry to the next, so the measure shifts a little even when no quote changes. On the days in the table that effect is small beside moves of several points. On quiet days it is not, which is one more reason to read the twelve days and not the quiet ones.
What does each rule do to the hedge?
Turn the three rules and the twelve day slope into a delta for the 23,200 call. The option's own volatility moves by R minus one skew slopes for a one percent rise, which is −1.10 points on the twelve day slope. The delta is the screen delta plus vega times that move, over one percent of the forward.
The more volatility moves with the index, the smaller the hedge
Appendix: the slope on the twelve days
slope = sum of (r x d)
/ sum of (r x r)
Here r is the index move in percent and d the change of the 30 day at the money volatility in points, for each of the twelve days in the table. The sum of products is −95.5 and the sum of squares 68.6, which gives −1.39. A line through the origin is the right shape here, because a day with no index move has no reason to carry a systematic volatility move. The delta hedging simulator under this page hedges an option at its screen delta along a seeded path. Use it to see how the hedge error builds when the volatility assumed differs from the volatility realised.
Read one more paragraph, 119 words
The ratios are 0.553 for sticky delta, 0.525 for sticky strike, 0.497 for local volatility and 0.423 for the twelve day slope. For a position of 100 option lots the screen delta, which is sticky strike, needs 52.5 lots of the future, sticky delta 55.3, local volatility 49.7 and the twelve day slope 42.3. The screen delta and the twelve day figure are 10.2 lots apart, and the two extremes 12.9. That spread is the size of the question. The future's lot and the option's lot are both 65 units, so lots map one to one. I take it as a measure of how much the assumption matters. I do not take it as an instruction.
The common mistake
The claim: Implied volatility stays put when the index moves, so the delta on the screen is the hedge ratio.
It did not stay put on any of those twelve big days. The screen delta holds each strike's volatility fixed, which is exactly the sticky strike rule, and on those days the at the money volatility moved about 4.7 times the skew slope where sticky strike allows one. On the twelve day slope the hedge ratio is 0.423 against the screen's 0.525. The honest statement is that the screen delta is the Black delta, one rule's answer, and that the hedge ratio that leaves the least variance depends on how volatility moves with the index in the window you are hedging through. I measure that window before I trust either number.
Key takeaways
- Sticky delta predicts zero change, sticky strike one skew slope, local vol two.
- The screen delta holds volatility fixed, so it is one rule, not the truth.
- On twelve large days the volatility moved against the index every time.
- The move was larger than any of the three rules predicts.
- One pair of dates mixes time and events, so it cannot pick a rule.
- Measure the regime in the window you hedge through.
Two terms to hold on to from 16.16
Before you trade. Derivatives trading carries a high risk of loss. SEBI's study "Profitability of Individual Traders in the Equity Derivatives Segment (FY25 to FY26)" (August 2026) found that 87.7% of individual traders in equity F&O made net losses in FY26, with aggregate net losses of Rs 91,685 crore. Read the SEBI study