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
- Compute a 25 delta risk reversal and butterfly from a dated NSE chain, and a slope per percent of strike.
- Explain why skew is quoted at a fixed delta and not at a fixed distance from the forward.
- 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 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
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
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 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
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
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
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.
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