What Is a Volatility Smile?
Volatility smile is the curve that appears when implied volatility is plotted against strike price. The standard model assumes one volatility for every strike, so the line should be flat. It is not: far strikes price in more movement, and in equities the curve skews downward.
The standard option-pricing model makes one assumption that can be checked directly against live prices. It fails, visibly, in every option chain on every exchange, and the shape of that failure has a name.
How to read it
Implied volatility is the movement a quoted option price implies. Take the market price, run the model backwards, and it returns one number: how much movement that price is assuming.
The model assumes one volatility for the underlying. Not one per strike — one, full stop. So plotting implied volatility against strike should produce a horizontal line.
It curves. Strikes far from the current price consistently imply more movement than strikes near it. Plotted, the middle sags and the edges lift — hence “smile.”
And this is not an anomaly to be arbitraged away. It is stable, persistent, and priced by professionals who understand the model perfectly well.
What the market knows that the model does not
The model assumes returns are normally distributed. Real returns are not — extreme moves happen far more often than a normal distribution allows, and they cluster rather than arriving independently.
So options at far strikes are worth more than the model says, because the events they pay out on are more likely than the maths assumes. Traders price that in by hand, and the smile is the visible result.
In equities the curve is lopsided. Downside puts imply more volatility than equivalent upside calls, because equity markets fall faster than they rise and everyone holding shares wants protection at the same time. That asymmetry is the skew, and it is the usual shape in stock options.
A worked example
This site’s shared series demonstrates why a flat assumption fails. The median bar range is 0.493 and the ninetieth percentile is 1.101 — one day in ten covers more than twice a typical one.
The largest single bar measured 2.338, about 4.7 times the median. Under a normal distribution built around a typical bar, a move that size is far rarer than once in a sample of this length.
So an option priced off the typical bar would be underpriced for the tails. The smile is the market correcting exactly that, strike by strike, without changing the model everyone still quotes from.
And volatility clustering makes it worse. Large moves arrive in runs, so the chance of several extreme days together is much higher than independent draws would give — which is precisely what a far strike pays out on.
Why the model is still used
Because it is a common language rather than a belief. Nobody thinks volatility is constant across strikes. The model is used to convert prices into a comparable number, and the smile is where the real opinion lives.
Quoting in implied volatility is more useful than quoting in currency. Two options on different strikes and expiries can be compared directly once both are expressed as implied movement.
So the smile is not the model failing quietly — it is the model being used as a unit of measurement while the market supplies the actual pricing on top.
The original data
On this site’s shared series: median bar range 0.493, ninetieth percentile 1.101, largest bar 2.338. Direction runs average 2.01 bars with a longest of 11.
The ratio between the median and the extreme is the whole argument. A factor of 4.7 between a typical bar and the largest one is a fat tail by any definition, and a pricing model assuming otherwise will underprice the strikes that pay out on it.
And every option trade still pays its round trip — 0.0098 here, about 2% of the median bar range — before any view on the smile has a chance to pay.
What a steep skew is actually telling you
That protection has become expensive, which is usually a statement about demand rather than about forecast risk. Everybody holding shares wants the same downside put at the same time, and there is no natural seller on the other side.
The steepness varies enormously by market. Index options carry a pronounced skew because index protection is in permanent institutional demand. Single stocks are flatter, and currencies are closer to a genuine symmetric smile because a move either way is a move against somebody.
It also moves with conditions. A calm market flattens the curve; turbulence steepens it, often sharply and in advance of price doing anything. That makes the shape one of the few things in markets that changes before the thing it is about.
And it is priced, which means it is a cost. Buying protection when the skew is steep means paying for a risk the market has already recognised — the insurance is dearest exactly when everyone wants it.
When it fails
The characteristic failure is treating a steep skew as a mispricing to be sold. Far downside puts look expensive against the model, so selling them appears to be collecting a premium the maths says is excessive. The maths is what is wrong. Those strikes are priced high because the events are genuinely more likely than a normal distribution allows, and the seller is collecting a fair price for a real risk — which pays reliably until the day it does not, and that day is the one the strike existed for.
A second failure is reading the smile as a forecast. It is a price, not a prediction, and a steep skew says what protection costs rather than what will happen.
A third is comparing skews across expiries without noting that the shape changes with time to expiry.
A fourth is assuming it is symmetric. In equities it almost never is; in currencies it is closer to a true smile.
And a fifth is trading the shape without the size to survive it. Positions built on skew are short tails by construction, and tails are what volatility clustering says arrive in runs.
Related
Volatility covers the measure the whole curve is expressed in. Volatility clustering covers why the tails are fatter than the model assumes. And technical analysis covers the wider set of tools this sits beside.
The volatility smile is my favourite thing in finance, because it is the market openly disagreeing with the textbook and doing so in every single quote. The standard model says one number should apply to every strike. Traders price otherwise, and they have been right to.
— Michael Whitman
This page is educational, not financial advice. Test every idea on your own charts before risking money.