Implied Volatility Intermediate IV across strikes Forward-looking

Volatility Smile

The shape Black–Scholes swore could not exist, printed on every option chain in the world.

Quick answer: The volatility smile is the U-shaped curve you get when you plot each strike's implied volatility against its strike price, in which both out-of-the-money puts and out-of-the-money calls print a higher implied volatility than the at-the-money option — evidence that the market prices fat tails on both sides that Black–Scholes assumes away.

In simple words

If Black–Scholes were the whole truth, every strike on the same expiry would print the same implied volatility, because the model treats volatility as a property of the underlying and not of the contract. Plot the implied volatility of each strike and you would get a flat horizontal line. You never do. Instead the line dips in the middle and rises at both ends: an option far below today's price and an option far above it both cost more — in volatility terms — than an option struck at the money. Drawn out, that curve looks like a smile, which is where the name comes from. It is the market telling you, in the only language it has, that big moves in either direction are more likely than the neat bell curve inside the model believes.

Take NIFTY at 24,000. The 24,000 strike might print an implied volatility of 13.5%. Go down to the 22,200 strike and it prints roughly 15%; go up to the 25,800 strike and it prints roughly 14.9%. Both wings are bid, and by a similar amount — that near-symmetry is the defining feature of a true smile, and it is why the smile is the honest, un-opinionated cousin of the skew. A currency pair like USD/INR prints this shape because a central bank can surprise the market in either direction with roughly equal force.

Not to be confused with: The volatility skew, which is what equity indices actually print. A skew is a smile that has been tilted so far to one side that the downside wing is permanently and dramatically higher than the upside wing. The smile is symmetric and says "big moves are underpriced"; the skew is lopsided and says "crashes specifically are underpriced". Confusing the two is the most common error in this whole section, because people learn "smile" first and then assume NIFTY has one.

The picture

The at-the-money strike sits at the bottom of the curve

Implied volatility of every strike in one expiry, spot at 24,000, plotted against strike.

The lowest implied volatility on the whole curve is the at-the-money strike, and every strike away from it in either direction prints higher. That is the shape Black–Scholes says cannot happen — the model assumes one flat line — and the fact that no liquid option market has ever printed that flat line is the strongest practical evidence that real returns have fatter tails than the lognormal distribution allows.

Professional explanation

The smile is a confession that the model is wrong

Black–Scholes derives an option's price from a single assumption about the underlying: that its returns are normally distributed with one constant volatility. Under that assumption, volatility belongs to the stock, not to the contract, so every strike and every expiry must share one implied volatility, and a plot of implied volatility against strike must be a flat horizontal line. The smile is the empirical fact that this line is never flat. Rather than abandon the formula — which is far too useful to abandon — the market keeps the formula and bends the input, quoting a different volatility for each strike so that Black–Scholes reproduces prices it could never have generated on its own. The smile is therefore not a feature of the world; it is the residue left behind when you force a wrong model to fit a right price. Every point above the bottom of the curve is a measure of how wrong the model is at that strike.

Why the at-the-money strike prints the lowest volatility

An at-the-money option's value comes almost entirely from the fat middle of the return distribution — the everyday moves that both the real world and the lognormal model agree are common. There is very little disagreement between model and market about how often NIFTY moves 1%, so the at-the-money strike needs only a small volatility adjustment and sits at the floor of the smile. An out-of-the-money option is the opposite: it only pays off in the tail, precisely the region where the lognormal model and reality diverge most. Real markets jump, gap and crash in ways a continuous bell curve forbids, so tail options are worth more than the model thinks. To force Black–Scholes to output that higher price, you must feed it a higher volatility. The further out of the money the strike, the more of its value lives in the mispriced tail, and the higher the implied volatility the market must quote — which is exactly why the curve rises away from the money in both directions.

Symmetry means no directional opinion

The defining property of a true smile, as opposed to a skew, is that its two wings are bid by roughly the same amount. That symmetry carries a specific message: the market fears a large move but has no strong view about which way it will go. This is what currency options genuinely print, because an exchange rate can be shocked in either direction — a central bank can cut or hike, an intervention can defend or devalue — and because the two counterparties to a currency are two economies, neither of which is structurally the "downside". Many individual stocks print a near-smile too, especially before a binary event like an earnings release or a court verdict, where the outcome is genuinely two-sided. The moment one direction becomes more feared than the other, the smile tilts, and you are looking at a skew.

The smile was born on a single day

Before October 1987, index options traded on a curve that was very close to flat — the smile, as a persistent feature of equity index options, essentially did not exist. On and after the crash of 19 October 1987, when the market fell more in one session than the lognormal model said was possible in the lifetime of the universe, the curve permanently changed shape and never went back. That historical fact is the single most important argument in this section, because it settles a debate: the smile is not a mathematical artefact of the Black–Scholes formula, nor a rounding error, nor a liquidity quirk. If it were any of those, it would have been there before 1987. It appeared the moment the market learned, expensively, that crashes are real — which means the smile encodes a belief about the world, not a bug in the arithmetic. That is a sentence a product marketing team would prefer you did not dwell on: the shape of every option chain is a scar.

The smile is one slice of a larger object

The same smile shape repeated across expiries becomes a surface.

A single smile is one expiry's slice through the volatility surface. Slide along the time axis and the smile flattens: the wings pull down toward the middle as expiry lengthens, because over a long horizon the sum of many daily returns starts to look more normal, and the fat tails that create the smile get averaged away.

Formula

A smile as a parabola in log-moneyness

σ(K) = σ_ATM + c · [ln(K / S)]²

A symmetric smile is well approximated by a parabola whose lowest point is at the money. Because the term depends only on the SQUARE of log-moneyness, the curve rises by the same amount whether you move a given distance up or down in log terms — that is the mathematical statement of symmetry, and it is what distinguishes a smile from a skew, whose defining term is linear in log-moneyness and therefore lopsided.

σ(K)Implied volatility of the option struck at K, expressed as an annualised decimal (0.135 = 13.5%).
σ_ATMThe at-the-money implied volatility — the minimum of the smile, the floor from which both wings rise.
cCurvature (convexity) of the smile. A larger c means steeper wings and a market pricing fatter tails. On the site's reference NIFTY chart c is about 2.6.
KStrike price of the option contract.
SSpot price of the underlying — 24,000 for NIFTY throughout this site.
lnThe natural logarithm. Log-moneyness ln(K/S) is used rather than K − S so that a strike and its mirror image (K/S and S/K) sit equal distances from the centre.

The convexity is the price of the tails

curvature ∝ excess kurtosis of the risk-neutral return distribution

The steepness of the smile is a direct read on how fat the market believes the tails are. A flat smile implies a normal distribution; a steep one implies heavy tails and frequent jumps. This is why volatility desks watch the CURVATURE of the smile, not just its level — the level tells you the price of movement, the curvature tells you the price of surprise.

How to read a volatility smile off a chain

Pick a single expiry and ignore all the others — a smile lives inside one expiry. Mixing expiries gives you a smear, not a smile.
For each strike, take the implied volatility from the bid-ask midpoint, not the last traded price, because on far strikes the last print can be hours stale and will spike the curve at exactly the point you care about.
Plot implied volatility on the vertical axis against strike (or log-moneyness) on the horizontal. Mark where spot is.
Find the bottom of the curve. On a true smile it sits at or very near the at-the-money strike; if it sits well below the money, you are looking at a skew, not a smile.
Compare the two wings. If the put wing and the call wing rise by similar amounts, it is a genuine symmetric smile and the market has no strong directional fear. If the put wing is far higher, it is a skew.
Read the curvature, not just the height. A deep, steep smile means the market is pricing fat tails and jump risk; a shallow one means it expects moves to stay closer to normal.
Sanity-check against the neighbours: a single strike that juts far above the smooth curve is almost always a stale or crossed quote, not a real dislocation.

Practical example

NIFTY worked example

Take one NIFTY expiry with spot at 24,000. The 24,000 at-the-money call prints an implied volatility of about 13.5% — the floor of the smile. Now walk out to the wings. The 22,200 put, roughly 7.5% below spot, prints about 15.0%. The 25,800 call, roughly 7.5% above spot, prints about 14.9%. Both wings are bid by roughly 1.4 to 1.5 volatility points over the middle, and — crucially — by almost the same amount on each side. Interpret that: the market is charging extra for a big move in either direction, and it is charging almost equally for up and down, so it fears magnitude without favouring a direction. If NIFTY actually printed this shape you would conclude the index was in a genuinely two-sided regime — perhaps ahead of an election count where the result could gap the market either way. The moment the put wing pulls decisively above the call wing, the smile has become a skew and the market has started fearing the downside specifically.

BANKNIFTY worked example

BANKNIFTY, being a concentrated basket of lenders, more often prints a skew than a clean smile — but around a binary sector event you can watch a smile briefly form. Suppose BANKNIFTY sits at 52,000 the day before an RBI policy decision that could plausibly cut or hold rates, with the market genuinely split. The 50,700 put and the 53,300 call — each about 2.5% from the money — might both print around 17.5% while the 52,000 straddle prints about 15.5%, a near-symmetric two-point smile. The lesson that differs from the NIFTY one: a smile can be a temporary, event-driven state even in a market that normally skews. When the policy is announced and the uncertainty resolves, the wings collapse and the curve tilts back to its habitual downward skew. A symmetric smile in an equity index is usually a snapshot of a genuinely undecided market, not its resting shape.

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.

Risk note. A steep smile is sometimes sold as a reason to short the wings — "the tails are overpriced, so sell them". They usually are overpriced on average, because tail insurance is sold above its expected cost. But the whole reason the smile exists is that the tail events it prices are real, and they arrive precisely when a short-wing position is largest and least liquid. Selling both wings of a smile is selling insurance against a disaster you have agreed to pay for in full when it happens. Short-option positions carry theoretically unlimited loss.

Advantages & limitations

What it is good for

It makes the failure of Black–Scholes visible and measurable. The gap between each strike's implied volatility and the at-the-money level is a direct, quotable measure of how far the market's beliefs depart from a normal distribution.
Its symmetry is instantly diagnostic. One glance tells you whether a market has a directional fear (a lopsided curve) or merely a fear of magnitude (a symmetric one), which is information no single volatility number can carry.
The curvature reads out the market's tail expectations. A steep smile prices heavy tails and jumps; a shallow one prices near-normal behaviour, so the smile lets you trade the fourth moment of the distribution, not just its width.
It is directly comparable across strikes on one expiry, which is what turns a list of option prices into a single legible shape a trader can reason about.
It gives event risk a picture. Before a genuinely two-sided binary event, a symmetric smile forms and then collapses, and watching it form is one of the cleanest ways to see the market pricing an event in real time.

Where it breaks down

It only describes one expiry. A smile is a single slice through the volatility surface, so it says nothing about term structure, and two expiries can print completely different smiles on the same underlying at the same instant.
It flattens with tenor, so a smile measured on a weekly option and a smile measured on a six-month option are not comparable shapes — the long-dated smile is shallower purely because of the central limit theorem, not because the market's beliefs changed.
Its wings depend on illiquid quotes. The deep strikes that define the shape of the smile are exactly the strikes where bid-ask spreads are widest and prints are stalest, so the extremities of the curve are the least reliable part of it.
It is model-relative. "The smile" means "the smile implied by Black–Scholes", and a different pricing model would extract a different curve from the same prices, so the smile is partly a property of the lens you view prices through.
It is rare in its pure symmetric form in equity indices. Assuming NIFTY prints a smile when it almost always prints a skew leads directly to mispriced hedges, because a symmetric model will systematically undercharge for the downside wing.

Common mistakes

Assuming NIFTY or any equity index prints a symmetric smile. It almost never does; it prints a skew. Building a hedge on a symmetric assumption undercharges for downside puts, which is exactly the wing that hurts you in a selloff.
Reading the height of the smile as bullish or bearish. The smile is direction-agnostic by construction — a bid call wing does not mean the market expects a rally, it means the market is charging for an up-move it does not predict.
Comparing the wings of a short-dated smile with the wings of a long-dated one and concluding the market's fear has changed. The long-dated smile is shallower because of the square-root-of-time averaging, not because anyone's beliefs shifted.
Trusting the extreme wings of the curve. The deepest strikes have the widest spreads and the stalest prints, so a smile that looks jagged at the edges is usually showing you quote noise, not a real kink in beliefs.
Concluding that a steep smile means the tails are overpriced and should be sold. The smile is steep because the market has priced real jump risk; selling that steepness is selling insurance against events that genuinely occur.
Treating the smile as fixed. It breathes — it steepens into events and fear, flattens into calm, and moves as spot moves, and a hedge calibrated to yesterday's smile is already slightly wrong today.

Professional usage

Volatility desks do not look at the smile to find the level of implied volatility — they have the at-the-money number for that. They look at the smile to price and risk-manage everything that is not at the money. A market maker fits a smooth, arbitrage-free smile through the quoted strikes and generates prices for every strike in between from that fitted curve, so the smile is literally the pricing engine for the illiquid strikes nobody quotes directly. The convexity of the fitted smile is itself a traded quantity: a desk that thinks the market is underpricing jump risk buys the wings and sells the middle — a butterfly in volatility terms — expressing a view on the curvature of the smile rather than its level or its slope.

Exotic-options desks care about the smile more than anyone, because the price of a barrier option, a digital, or a cliquet depends on the whole shape of the return distribution, not just its width — and the shape is exactly what the smile encodes. A digital option that pays a fixed amount if NIFTY finishes above a strike is, to first order, the slope of the vanilla smile at that strike; get the smile shape wrong and you misprice and mishedge the digital. This is why quant desks spend so much effort on smile-consistent models: the smile is not decoration, it is the boundary condition every exotic must respect.

Key takeaways

The volatility smile is the U-shaped plot of implied volatility across strikes for one expiry, with the at-the-money strike at the bottom and both wings bid.
It exists because real returns have fatter tails than the lognormal distribution inside Black–Scholes, so out-of-the-money options are worth more than the model thinks and must be quoted at a higher implied volatility.
A symmetric smile carries no directional opinion — it prices magnitude, not direction — and is what currency options and pre-event single stocks genuinely print.
The equity-index smile essentially did not exist before the October 1987 crash and has never gone away since, which is strong evidence the shape encodes a belief about crashes rather than a modelling artefact.
The at-the-money strike prints the lowest volatility because its value lives in the fat middle of the distribution where model and reality agree; the wings live in the tails, where they do not.

Learn to see the smile as the market's correction to a formula it cannot bring itself to discard. Black–Scholes gives one flat line; reality gives a curve; the smile is the difference, quoted strike by strike, and its height at each point is a measure of exactly how much the real distribution's tails outweigh the model's. Read it as a shape, not a number: the level is the price of movement, the tilt is the price of direction, and the curvature is the price of surprise. Once you see it that way, the smile stops being a curiosity and becomes the most information-dense picture on the entire option chain.

Frequently asked questions

What is a volatility smile in simple terms?

A volatility smile is the U-shaped curve you see when you plot each option strike's implied volatility against its strike price. Out-of-the-money puts and calls both print higher implied volatility than the at-the-money option, so the line dips in the middle and rises at both ends, like a smile. It exists because the market prices big moves as more likely than Black–Scholes assumes.

Why does the volatility smile exist?

It exists because real asset returns have fatter tails than the normal distribution Black–Scholes assumes, so out-of-the-money options — which only pay off in those tails — are worth more than the model computes. To force the model to reproduce their higher market prices, you feed it a higher volatility, and doing that at every strike traces out the smile.

Why is the implied volatility lowest at the money?

Because an at-the-money option's value comes from the fat middle of the return distribution, where Black–Scholes and reality broadly agree, so it needs almost no volatility adjustment. Out-of-the-money strikes derive their value from the tails, where model and reality diverge most, so they need a larger upward adjustment — pushing the wings above the middle.

What is the difference between a volatility smile and a volatility skew?

A smile is symmetric — both wings rise by roughly the same amount, so it prices magnitude without a directional view. A skew is lopsided — the downside put wing is systematically higher than the upside call wing, so it prices crashes specifically. Equity indices print skews; currencies and many pre-event single stocks print smiles.

Do NIFTY options have a volatility smile?

Usually not a symmetric one — NIFTY, like most equity indices, prints a downward skew, with out-of-the-money puts dearer than out-of-the-money calls. A near-symmetric smile can appear briefly around a genuinely two-sided binary event, but the index's resting shape is a skew, and assuming otherwise leads to under-hedged downside.

Which markets actually print a symmetric smile?

Currency options are the classic example, because an exchange rate can be shocked in either direction with roughly equal force and neither side is structurally the downside. Many individual stocks print a near-smile ahead of a binary event such as earnings or a verdict, where the outcome is genuinely two-sided.

When did the volatility smile first appear?

The equity-index smile essentially did not exist before October 1987 — index options traded on a nearly flat curve. The crash of 19 October 1987 permanently changed the shape, and it never reverted. That timing is strong evidence the smile encodes a learned belief about crashes rather than a mathematical artefact of the pricing formula.

What does the steepness of a smile tell you?

The curvature of the smile reads out how fat the market believes the return tails are. A steep smile prices heavy tails and frequent jumps; a shallow one prices near-normal behaviour. That is why desks watch the curvature separately from the level — the level is the price of movement, the curvature is the price of surprise.

Does a volatility smile predict market direction?

No. A symmetric smile is direction-agnostic by construction — it charges extra for a large move without favouring up or down. A bid call wing does not mean the market expects a rally; it means the market is pricing an up-move it does not predict. Only a tilt in the smile, turning it into a skew, carries directional information.

Why does the smile flatten for longer-dated options?

Because of the central limit theorem. A long-dated return is the sum of many daily returns, and sums of many independent-ish moves tend toward a normal distribution, so the fat tails that create the smile get averaged away. The long-dated smile is therefore shallower than the short-dated one even when the market's beliefs have not changed.

Is the volatility smile evidence that Black–Scholes is wrong?

Yes, directly. Black–Scholes assumes one constant volatility, which forces every strike to share one implied volatility and the plot to be flat. The smile is the empirical fact that the plot is never flat. It is the residue left behind when you force a wrong model to fit right prices, quoted strike by strike.

How do you measure the convexity of a smile?

Practically, by fitting a curve — often a parabola in log-moneyness or a spline — through the quoted strikes and reading its curvature, or by comparing the average of the two wings against the at-the-money level (a volatility butterfly). A larger butterfly value means a steeper, more convex smile pricing fatter tails.

Can the volatility smile be traded?

Yes, through combinations that isolate its shape. A volatility butterfly — long the wings, short the middle — expresses a view that the smile is too flat or too steep, independent of the overall level of implied volatility. This is distinct from trading the skew, which is a bet on the smile's tilt rather than its curvature.

Why do the wings of the smile look jagged sometimes?

Because the deep out-of-the-money strikes that define the wings are the least liquid, with the widest bid-ask spreads and the stalest last-traded prices. A single stale or crossed quote spikes the curve at exactly the extremity you care about, so jaggedness at the edges is usually quote noise, not a real feature of beliefs.

Does the volatility smile change over time?

Constantly. It steepens into events and into fear, flattens into calm, and shifts as spot moves. A smile is a live object, not a fixed curve, which is why a hedge calibrated to yesterday's smile is already slightly wrong today and why desks re-fit the curve continuously.

What is the relationship between the smile and fat tails?

They are two descriptions of the same fact. Fat tails mean extreme returns are more likely than a normal distribution says; the smile is what that excess probability looks like once it is priced into out-of-the-money options and expressed in volatility terms. A steeper smile corresponds to fatter tails and higher excess kurtosis.

How does the smile relate to the volatility surface?

A smile is a single expiry's slice through the volatility surface. Stack the smiles of every expiry side by side and you get the two-dimensional surface of implied volatility over strike and time. The smile is the strike dimension; the term structure is the time dimension; together they are the surface.

Why do currency options have a symmetric smile but stocks do not?

Because a currency is a ratio of two economies, either of which can be shocked, so there is no structural downside — a smile is the natural symmetric result. An equity index has a structural downside: it falls faster than it rises and everyone hedges the same crash, which tilts the curve into a skew.

Is a higher smile always more expensive to trade?

A higher smile means richer wings, so buying out-of-the-money options costs more in volatility terms. But "expensive" is only meaningful relative to what the underlying subsequently does. A steep smile that correctly anticipates a jump was cheap in hindsight; a steep smile in a market that stays calm was expensive. The shape is a price, not a verdict.

What is the volatility smile for at-the-money options specifically?

The at-the-money strike sits at the very bottom of the smile — it is the minimum of the curve and the conventional reference point when anyone quotes "the" implied volatility of an underlying. Every other strike on the same expiry prints higher, and how much higher, moving outward, is precisely the smile.

Voice search & related questions

Natural-language questions people ask about volatility smile.

Why is it called a smile?

Because when you plot implied volatility against strike, the curve dips in the middle at the at-the-money strike and rises at both ends where the out-of-the-money options are, tracing a shape that looks like a smiling mouth. The name is purely descriptive of the picture on the chart.

Does NIFTY have a smile or a skew?

NIFTY normally has a skew, not a symmetric smile — its out-of-the-money puts are dearer than its out-of-the-money calls because the index fears a crash more than a melt-up. A symmetric smile only appears briefly around genuinely two-sided events. Assuming NIFTY smiles is a common and costly beginner error.

Why do out-of-the-money options cost more in volatility terms?

Because they only pay off in the tails of the return distribution, and real markets have fatter tails than Black–Scholes assumes, so those options are worth more than the model computes. Feeding the model a higher volatility is the only way to make it reproduce their true market price.

Is a steep smile a warning sign?

It tells you the market is pricing fat tails and jump risk more heavily than usual, which often accompanies nervousness. But it is not a prediction — a steep smile can persist for a long time in a market that stays calm, and it can flatten just before a shock. It is a price for surprise, not a forecast of one.

Can I make money selling the wings of a smile?

Selling the wings collects the premium the market charges for tail risk, which is positive on average because insurance sells above its expected cost. But the tails the smile prices are real and arrive when your short position is largest and least liquid, and short options carry theoretically unlimited loss. This is not investment advice.

What does it mean when the smile suddenly flattens?

A flattening smile means the market is charging less for the wings relative to the middle — it is pricing calmer, more normal behaviour and less jump risk. This often happens after a feared event passes without incident, when the tail insurance everyone bought is no longer needed and gets sold back.

How is the smile different for weekly versus monthly options?

The weekly smile is steeper and the monthly smile is shallower, because over a longer horizon daily returns average toward a normal distribution and the fat tails fade. So you cannot compare the two shapes directly — the weekly always looks more dramatic, and that is arithmetic, not a difference in market view.

Sources & references

Last reviewed 10 July 2026. Educational content only — not investment advice.