Volatility Smile

Q: What is the volatility smile?

The volatility smile is the shape you get when you plot implied volatility against strike price for options of one expiry. Instead of the flat line the Black-Scholes model assumes, implied volatility is lowest near the at-the-money strike and rises toward both far-out-of-the-money puts and calls, giving a U shape. On equity indices the left side is usually higher, so the curve looks like a lopsided smile or a smirk.

Q: Why does the smile exist if the model says IV should be constant?

Because real index returns are not lognormal with constant volatility. Markets fall faster than they rise, large moves happen more often than a normal distribution predicts, and volatility itself changes. Option prices reflect those features, and when you force each price through the Black-Scholes formula the only free input, implied volatility, has to differ by strike to make the prices fit.

Q: What is the difference between a smile and a skew?

The smile is the whole curve. The skew is its tilt, the difference between put-side and call-side implied volatility. A symmetric U is a pure smile, common in currencies. Equity indices such as NIFTY show a skewed smile where out-of-the-money puts carry much higher IV than equally distant calls, because demand for downside protection is persistent.

Q: How do I read the smile from the option chain?

Take one expiry and note the IV column strike by strike. Find the minimum, usually at or just above the spot, then see how fast IV climbs on each side. A steep left side means the market is paying up for crash protection; a flattening left side means that fear is easing; a right side that lifts means demand for upside calls, often before a rally or an event.

Q: Does the smile change over time?

Yes. It steepens when the market is nervous and flattens when it is calm, and it is more pronounced on short-dated expiries than on long ones. Comparing today's smile to last week's is a standard way to read how positioning and fear have shifted, independently of the overall level of volatility.

One expiry, many strikes, and a different implied volatility at each. The curve that results is the market's own correction to the pricing model, and it is readable straight off the chain.

In short: the volatility smile is the curve you see when you plot implied volatility against strike for a single expiry. The pricing model assumes one volatility for every strike; the market prices a curve instead, lowest near the money and rising toward the wings. On NIFTY and other equity indices the curve tilts so that out-of-the-money puts carry higher IV than equally distant calls, which is the skew. The smile tells you what the market fears, in which direction, and how much it is paying for it.

The intuition

Implied volatility is the number you back out of an option's market price with the Black-Scholes formula. If the model described the world exactly, every strike on the same underlying and expiry would give the same number, because they all look at the same future. In practice they do not. Deep out-of-the-money options trade at prices too high for a constant-volatility world, so solving each for IV produces a higher figure at the wings than at the centre. Plot them and you get a smile.

The reason is in the returns themselves. Index returns have fat tails: moves of three or four standard deviations happen far more often than the model's bell curve allows. They are also asymmetric: falls are faster and larger than rises, and volatility rises when prices fall. An option that pays only in those tails is worth more than the model thinks, and the market knows it. Since the formula has only one free input, the correction shows up as a strike-dependent IV.

The shape on an Indian index

On NIFTY the curve is not a symmetric U. The left side, the put side, is steep: a put 1,000 points below spot might carry five IV points more than the at-the-money option, while a call 1,000 points above carries one or two points less. The minimum of the curve usually sits at or slightly above spot. This is the equity smirk, and it comes from one-sided demand. Portfolio holders buy puts for protection and sell calls for income, so puts are bid and calls are offered, persistently.

Worked example (illustrative numbers)

Suppose NIFTY is at 24,000 with 27 days to the monthly expiry, and the chain shows these implied volatilities:

Strike	IV	Put premium	Call premium
23,000	19.0%	₹118	₹1,228
23,500	16.5%	₹186	₹799
24,000	14.0%	₹309	₹424
24,500	12.5%	₹554	₹172
25,000	12.0%	₹934	₹54

The 23,000 put and the 25,000 call are both 1,000 points from spot, but the put costs ₹118 and the call ₹54. At a flat 14% the put would be worth about ₹46 and the call about ₹86; the smile has more than doubled the put and cut the call by more than a third. That is the market's statement that a 1,000-point fall in 27 days is far more likely, or far more costly to be caught in, than a 1,000-point rise. Note that the premiums still obey put-call parity at every strike; the smile changes the level of both put and call at a strike together, not their difference.

The equity smirk: steep on the put side, gentle on the call side, lowest near the money. The dashed line is what a constant-volatility model would show.

Why it matters to an options trader

It prices every spread you trade. A put spread sells a higher-IV strike against a lower one; a call spread does the opposite. The smile decides whether a spread is cheap or dear before you look at the direction.
It is a sentiment gauge independent of the VIX. India VIX gives the level of volatility; the smile gives its shape. A rising VIX with a steepening put side is fear; a rising VIX with a lifting call side is a chase.
It moves your Greeks. Because IV differs by strike, an option's delta and vega computed at the market IV differ from the flat-vol figures. Hedging a book across strikes needs the curve, not one number.
It is where "cheap" and "expensive" live. A strike whose IV sits above its usual position on the curve is rich relative to its neighbours, whatever the overall level.

Common mistakes

Using the at-the-money IV for every strike. It underprices far puts badly. Price each strike at its own IV.
Calling a put the "same" as an equidistant call. On an index they are not; the put carries a structural premium.
Reading a steep smile as a prediction of a crash. It is the price of insurance, which is high even in long calm markets. Its change over time carries more information than its level.
Selling the wings because their IV is "high". The wings are high for a reason; naked short far-out options collect little premium against the move that the smile is pricing.
Comparing smiles across expiries. Short expiries have steeper, more curved smiles than long ones. Compare like with like, or use the surface.

Indian-market specifics

The NIFTY weekly (Tuesday) has the most pronounced smile on the chain; the monthly is flatter, and far-month expiries are often too thinly traded for the curve to be reliable at the wings.
The put-side steepness widens before budgets, elections and RBI policy days and compresses after them; the call side lifts during strong momentum phases.
NSE's published implied volatility for each strike is computed from the last traded price and can be stale at illiquid strikes; a mid-price IV is more trustworthy for the shape.
Stock options show individual smiles that depend on the stock's own event risk; the index smile is the composite of positioning, not a single stock's news.

FAQ

What is the volatility smile?

The curve of implied volatility against strike for one expiry, lowest near the money and rising toward the wings.

Why does the smile exist if the model says IV should be constant?

Because real returns have fat tails and fall faster than they rise. The formula's one free input absorbs the difference.

What is the difference between a smile and a skew?

The smile is the whole curve; the skew is its tilt toward the put side.

How do I read the smile from the option chain?

Take the IV column for one expiry, find the minimum, and watch how fast it rises on each side and how that changes day to day.

Does the smile change over time?

Yes: it steepens in nervous markets, flattens in calm ones, and is always sharper on short expiries.

The smile on today's chain

The NIFTY option-chain page lists the implied volatility at every strike for the current expiry, so the curve can be read strike by strike. In the app, the option chain shows the Greeks and implied volatility at every strike for the selected expiry.

NIFTY option chain IV guide

Related terms

Volatility Skew, the tilt of the smile and how to trade it
Volatility Surface, the smile across every expiry at once
Implied Volatility, the number being plotted
Black-Scholes Model, the model the smile corrects