---
title: "Skew measures: 25 delta risk reversal, Nifty options"
description: "Risk reversal, butterfly and slope read off dated NSE chains: Nifty on a calm day and a stress day, BANKNIFTY and a stock, with the delta convention stated."
source_url: "https://www.rupeecase.com/learn/path-16/module-16-8-skew-measures"
---

[Path 16 8 of 16](/learn/path-16/)Skew measures: risk reversal, butterfly and slope[Next 16.9](/learn/path-16/module-16-9-term-structure-and-event-variance)

Wednesday 10 Jun 2026. The Nifty June monthly future settled at 23,240.10 and the at the money implied volatility was 15.03%. Two options sat at about 25 delta, one on each side. The 22,700 put, delta 0.25, implied 15.74%. The 23,800 call, delta 0.24, implied 14.38%. Call vol less put vol: −1.36 points. That is the risk reversal. On 7 Apr 2025, with India VIX at 22.79, the same reading was −10.13. A smile is a picture. This module turns it into numbers you can set side by side, and shows where those numbers go wrong. Every figure comes from NSE end of day files, dated, so nothing here is live and nothing is a view on where Nifty goes next.

3By the end you can

1. Compute a 25 delta risk reversal and butterfly from a dated NSE chain, and a slope per percent of strike.
2. Explain why skew is quoted at a fixed delta and not at a fixed distance from the forward.
3. Say which delta, expiry and price a skew number uses before you set it beside another.

## The idea, plainly

### What are risk reversal, butterfly and slope?

The [smile and skew module](/learn/path-16/module-16-7-volatility-smile-and-skew) drew the curve of implied volatility across strikes. Here I measure it. Read the implied volatility at two wings, one on each side of the forward, and two differences describe most of the shape.

Risk reversal =
call wing vol
less put wing vol

Butterfly =
average of the two wings
less at the money vol

Slope = put wing vol less
call wing vol, divided by
the gap between the two
strikes, in percent

Read 3 more paragraphs, 140 words
The risk reversal is the tilt. It is negative when puts are richer than calls, which is the usual lean for an equity index. The butterfly is the bend. It is positive when both wings sit above the middle. A third number, the slope, is the tilt again but per percent of strike distance.

Slope earns its place because the first two depend on where the wings sit. Slope does not, as long as the strikes are written next to it.

A word on sign. Desks quote the risk reversal as call vol less put vol, so the Nifty number is negative. Some screens quote put less call and show a positive number. I use call less put in the text, and the bars in the charts show put less call, so that longer bars mean a richer put wing.

### Why fix the delta and not the distance?

Because the same distance means different things on different days. On 10 Jun 2026 the 22,250 put sat 4.3% below the forward and had a delta of 0.13. On 7 Apr 2025 the 21,300 put sat 4.3% below its forward and had a delta of 0.25. The same distance gave about twice the delta, because volatility was higher and the strike was nearer the money in the option's own terms. A fixed delta puts both days at the same place on each side. That is why desks quote a 25 delta or a 10 delta risk reversal and not a four percent one.

The term this section turns on: Risk reversal

From the module glossary; every term is in the Learn glossary too. Source: Module 16.8, Skew measures: risk reversal, butterfly and slope.

### What moves skew?

Three explanations circulate, and one chain cannot separate them. Holders of shares buy puts as insurance, and that demand lifts put prices. Index falls tend to arrive faster than rises, so the left tail is fatter than the lognormal curve behind Black 76 allows. And volatility tends to rise when the index falls, so a put pays most in the states where vol is already high. Each is a story about demand or risk, not a rule that holds every day. What the three numbers can do is say how big the tilt was that evening, and how it compares with other evenings read the same way.

Three numbers come from one pair of wings

A sketch of the method, not a market number. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
The maths: delta, the strike at a delta and the conventions
The delta used here is the Black 76 forward delta, taken on the future and including the discount factor.

Call delta =
e^(-rT) x N(d1)

d1 = [ln(F/K) + s^2 T / 2]
/ (s x sqrt(T))

A 25 delta call is the strike where that delta is 0.25, and a 25 delta put is the strike where the put delta is minus 0.25. The catch is that the volatility s is itself a function of the strike. So the strike is found by trial on the smile, not by a formula. The engine behind the tool does that and interpolates between listed strikes. This page takes the listed strike whose delta rounds closest to the target, and prints that delta, so the numbers can differ from the tool in the second decimal.

Three conventions are in use. Forward delta, used here. Spot delta, from Black Scholes on the spot index; it equals the forward delta times the future over spot, and at these expiries that ratio is within a fraction of a percent of one. And the premium adjusted delta of currency options, which I do not use for index options. Name the one you used. A fourth way avoids delta altogether and fixes moneyness, such as strikes five percent either side of the forward.

A skew number divided by the at the money vol, risk reversal over at the money, gives a normalised tilt that compares a quiet day with a stressed one on the same scale.

## Worked example: four dated chains

### What do the three numbers say on a calm day?

Take the June monthly of 10 Jun 2026. At the money is the future, 23,240.10. The two wings are the listed strikes whose delta is nearest 0.25.

| 10 Jun 2026 | Strike, delta size | Implied vol |
| --- | --- | --- |
| Put wing | 22,700, 0.25 | 15.74% |
| At the money | 23,240.10 | 15.03% |
| Call wing | 23,800, 0.24 | 14.38% |

Read one more paragraph, 172 words
The put wing is 2.3% below the forward and the call wing 2.4% above it. The risk reversal is −1.36 points. The butterfly is 0.03: almost no bend. The put cost 133.70 a unit and the call 111.40, a lot of 65 units each. On this chain the tilt came with next to no bend. In rupees, at the settlement prices, the put wing cost Rs 8,691 a lot and the call wing Rs 7,241. Desks use the name risk reversal for the position too: a call and a put at the same delta, one bought and one sold. The quote is that pair's price in vol terms, and the vol gap is why the two premiums differ. Both wings traded, the put in 12,942 contracts and the call in 27,674, so both vols come from trades and not from the exchange's model settlement. A wing with no volume is dropped from the smile. The [implied volatility solver module](/learn/path-16/module-16-3-solving-for-implied-volatility) shows how each vol is found from its price.

### What changes on a stress day?

Now 7 Apr 2025, India VIX 22.79 and the at the money vol 25.04%. The wings at about 25 delta are the 21,300 put, 4.3% below the forward, at 31.73%, and the 23,000 call, 3.3% above it, at 21.60%. The risk reversal is −10.13. The butterfly is 1.62. The whole curve moved up and the left side moved most. Two cautions. It is one chain on one evening. And the level of vol rose too, so the tilt is also read as a share of the at the money vol: −0.40 against −0.09 on the calm day. It grew even after scaling.

The stress day curve is higher and far steeper on the left

Implied volatility of the out of the money option at each strike that traded, within ten percent of the forward. Expiries 30 Jun 2026 and 24 Apr 2025. Percent a year. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
The tilt was 7.4 times the calm day's. Read at a fixed distance instead, the number would mix two effects: the tilt, and how near the money the wings sit.

### What about BANKNIFTY and a stock?

BANKNIFTY on 10 Jun 2026 sat between the two Nifty days: at the money 18.96%, the 53,500 put at 20.45% and the 56,800 call at 17.55%, a gap of 2.90. A large private bank stock on the same day, at the money 23.52%, leaned the other way. Its 770 call read 26.33% and its 715 put 23.19%: a risk reversal of 3.14, with a butterfly of 1.24. The sign of a skew belongs to one underlying on one date.

At 25 delta the stress day gap is the widest of the three

Put wing less call wing, the risk reversal with its sign flipped. Nearest listed strikes to 25 delta. Implied volatility computed by RupeeCase from NSE settlement prices. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.

### Does the expiry matter?

Yes, and fixed delta hides it. On the same evening the July monthly, 48 days out, has its 25 delta wings further from the forward: the 22,500 put is 3.6% below and the 24,200 call 3.7% above. The put reads 16.03% and the call 13.92%, so its risk reversal widens to 2.11, against 1.36 for the June monthly, 20 days out. The smile per percent of strike barely moved. The slope between strikes about five percent either side is 0.28 vol points per percent for June and 0.29 for July. A longer expiry puts a fixed delta further out, so its risk reversal grows even when the curve per percent does not. Compare risk reversals at one expiry, or use slope.

### Four things to write beside a skew number

A skew number alone is half a fact. These four turn it into a whole one.

* The delta of the wings, or the strikes if the wings are fixed by moneyness.

* The expiry, because a fixed delta moves out as time grows.

* The price behind each vol: settlement, last trade or mid.

* The sign: call less put, or put less call.

## The common mistake

The claim: The Nifty skew is 2.81 on my screen and 1.36 on your page, so one of us has it wrong. Neither has to be. On the 10 Jun 2026 June monthly the 25 delta pair gives 1.36 points, the 10 delta pair, the 22,100 put at 17.30% and the 24,300 call at 14.49%, gives 2.81, and the 22,100 put and the 24,400 call at 14.57%, 4.9% below and 5.0% above the forward, give 2.73. One chain, one evening, three honest answers.

One chain, three definitions, three skews

Nifty June monthly, 10 Jun 2026. Nearest listed strikes. Implied volatility computed by RupeeCase from NSE settlement prices. Source: NSE end of day data, computed by RupeeCase. As of 10 Jun 2026.
Read one more paragraph, 51 words
So I write the four items above beside every skew number I keep. Skew is also a price, not a prediction. A gap of 10.13 points on 7 Apr 2025 is what protection cost that evening, after the fall had happened. It does not say how far the next move goes.

## Key takeaways

* Risk reversal is the tilt of the smile. Butterfly is its bend.
* Fix the delta, not the distance, so chains of different volatility compare.
* Nifty put wings carried the higher vol on both index days here.
* The stress day's gap was several times the calm day's.
* One chain gave three different skews under three definitions.
* Skew prices protection. It is not a forecast of a fall.

Watch in the terminal: how bumpy was the ride? A short tutorial on sample data.
**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](https://www.sebi.gov.in/reports-and-statistics/research/aug-2026/study-profitability-of-individual-traders-in-the-equity-derivatives-segment-fy25-fy26-_103835.html)

What does Skew measures: risk reversal, butterfly and slope cover?A smile is a picture. Three numbers read at a fixed delta turn it into something you can compare across days, expiries and underlyings. It works through The idea, plainly, Worked example: four dated chains, The common mistake, Key takeaways. It is module 16.8 of Path 16, Volatility, about 10 minutes of reading, free.

TTry it

## IV solver, on the same example.
The implied volatility behind a dated settlement price. Dated NSE end of day data, nothing live, no orders.

**IV solver**, Nifty, 10 Jun 2026, 30 Jun 2026 expiry.

[Open the iv solver](/learn/tools/iv-solver?chain=NIFTY_2026-06-10_2026-06-30)

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QQuick check

## 10 questions, 7 to pass.
Each attempt draws 10 of the 15 questions in this module's bank, and a retake draws a fresh set. A pass gives this module's Certificate of Completion. Your result stays on this device and counts towards the Path 16 certificate.

7 of 10 correct passes module 16.8

Every answer is explained when you check; a retake is always free. Source: RupeeCase Learn quiz rules (70% to pass).

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###

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CCheck yourself

## Path 16 so far.
Your quick check results on this device, stop by stop.

Stop 8 of 16 on Path 16

Volatility: every live stop, this module ringed. Source: RupeeCase Learn, Path 16.

1. [16.1Volatility: historical against impliedNot yet](/learn/path-16/module-16-1-historical-vs-implied-volatility)
2. [16.2India VIX for beginners: what it measures and what it does notNot yet](/learn/path-16/module-16-2-india-vix-explained)
3. [16.3Solving for implied volatilityNot yet](/learn/path-16/module-16-3-solving-for-implied-volatility)
4. [16.4IV rank and IV percentile, done properlyNot yet](/learn/path-16/module-16-4-iv-rank-and-iv-percentile)
5. [16.5Measuring realised volatility: four estimatorsNot yet](/learn/path-16/module-16-5-realised-volatility-estimators)
6. [16.6Events and IV crush: results, Budget, RBI and electionsNot yet](/learn/path-16/module-16-6-iv-crush-around-events)
7. [16.7Smile and skew: a first look at Nifty and stocksNot yet](/learn/path-16/module-16-7-volatility-smile-and-skew)
8. [16.8Skew measures: risk reversal, butterfly and slopeNot yet](/learn/path-16/module-16-8-skew-measures#quiz)
9. [16.9Term structure and event varianceNot yet](/learn/path-16/module-16-9-term-structure-and-event-variance)
10. [16.10Forward volatility from two expiriesNot yet](/learn/path-16/module-16-10-forward-volatility)
11. [16.11India VIX rebuilt step by stepNot yet](/learn/path-16/module-16-11-india-vix-rebuilt)
12. [16.12Forecasting volatility: EWMA, GARCH and HARNot yet](/learn/path-16/module-16-12-forecasting-volatility)
13. [16.13The variance risk premium in NiftyNot yet](/learn/path-16/module-16-13-variance-risk-premium)
14. [16.14Variance swaps and replicationNot yet](/learn/path-16/module-16-14-variance-swaps)
15. [16.15Volatility surface models: SVI, SABR, local and stochastic volNot yet](/learn/path-16/module-16-15-volatility-surface-models)
16. [16.16Skew dynamics: sticky strike against sticky deltaNot yet](/learn/path-16/module-16-16-skew-dynamics)
17. [TPath test, 30 questionsNot yet](/learn/path-16/module-16-16-skew-dynamics#pathTestSection)

Path 16 in reading time: 159 minutes over 16 modules

Minutes of reading per module, this one in amber. Source: RupeeCase Learn, Path 16.

    Explore next

## Put the module to work.

* [ToolOption payoff builderLegs on a dated Nifty chain, breakevens and charges](/learn/tools/payoff-builder)
* [Free module 16.7Smile and skew: a first look at Nifty and stocks8 min read](/learn/path-16/module-16-7-volatility-smile-and-skew)
* [Free module 16.3Solving for implied volatility9 min read](/learn/path-16/module-16-3-solving-for-implied-volatility)
* [Free module 16.6Events and IV crush: results, Budget, RBI and elections9 min read](/learn/path-16/module-16-6-iv-crush-around-events)
* [Free module 16.9Term structure and event variance10 min read](/learn/path-16/module-16-9-term-structure-and-event-variance)
* [Free module 16.10Forward volatility from two expiries10 min read](/learn/path-16/module-16-10-forward-volatility)

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SSources

## Go to the source.
6 sources, NSE the most cited

The publisher of each source listed below. Source: Module 16.8 source list.
1. [NSE, option chain (Nifty 50 index options)](https://www.nseindia.com/option-chain) NSE
2. [NSE, derivatives end of day reports: the F&O bhavcopy these figures are built from](https://www.nseindia.com/all-reports-derivatives) NSE
3. [NSE, India VIX: index page and methodology](https://www.nseindia.com/static/products-services/indices-indiavix-index) NSE
4. [NISM, Series VIII Equity Derivatives, test objectives (option pricing, volatility and option strategies)](https://www.nism.ac.in/revamp-nism/test-objectives-revised-nism-series-viii-equity-derivatives-certification-examination/) NISM
5. [SEBI investor education, Understanding derivatives](https://investor.sebi.gov.in/understanding_derivatives.html) SEBI
6. Bennett, C. (2014), Trading Volatility: Correlation, Term Structure and Skew Book

GTerms

## 5 terms from this module.
Risk reversalThe implied volatility of the out of the money call less that of the out of the money put, both at the same delta. Negative means puts are richer.
Butterfly (smile)The average implied volatility of the two wings less the at the money implied volatility. Positive means both wings sit above the middle.
WingAn out of the money option far from the forward, on the put side or the call side, read at a chosen delta.
Forward deltaThe Black 76 delta taken on the future, with the discount factor included. A 25 delta call is the call whose forward delta is a quarter.
SlopeThe change in implied volatility per percent of strike distance, near the money. It compares expiries that fixed delta cannot.
[All 230 terms in the glossary](/learn/glossary)

[Question people askVolatility smile or skew: what is the difference?A short answer with a dated chart](/learn/questions/volatility-smile-vs-skew)[Question people askWhy are Nifty OTM puts pricier than calls?A short answer with a dated chart](/learn/questions/why-otm-puts-cost-more)[Related module16.7 Smile and skew: a first look at Nifty and stocks8 min, Intermediate](/learn/path-16/module-16-7-volatility-smile-and-skew)[Related module16.3 Solving for implied volatility9 min, Intermediate](/learn/path-16/module-16-3-solving-for-implied-volatility)[Pillar guideDerivatives and Quant115 modules across paths 12 to 19](/learn/derivatives)

Education only, not investment advice, a research report or a recommendation to buy, sell or hold any security. RupeeCase (QC Alpha Technologies Pvt Ltd) is not registered with SEBI as an investment adviser or research analyst. Contracts and prices shown are for illustration only, come from NSE end of day files at least 30 days old, and are not recommendatory. Derivatives trading carries a high risk of loss.