What is the volatility smile?

What the model gets wrong

The Black-Scholes model assumes that returns are normally distributed with constant volatility. Under that assumption, a single volatility number should price every strike on an expiry, and a plot of implied volatility against strike would be a flat line.

Markets do not cooperate. Large moves happen far more often than a normal distribution allows. A five-standard-deviation day, which a normal curve treats as almost impossible, turns up in real market history far more often than that. Options far from the money are the ones that pay off in those moves, so if the market priced them with the flat-line volatility, sellers would be under-compensated. Instead, traders mark those strikes at higher implied volatility, and the curve bends.

The smile is therefore not a flaw in the market; it is the market correcting a flaw in the model. Implied volatility at each strike is simply the number that makes the model's price match the market's price.

Smile, smirk and skew

A pure smile, roughly symmetric with both wings elevated, is most common in currency options and in single stocks heading into binary events, where a large move in either direction is plausible. A takeover target or a company awaiting a regulatory decision can show a pronounced smile.

Equity indices show a lopsided version, often called a smirk or simply skew: the put wing is far higher than the call wing, which may barely rise at all. The extra downside premium reflects crash risk and the steady institutional demand for protection.

The terms are used loosely. Many traders say smile for any curved shape and skew for the slope between the wings. What matters is the shape itself: which wing is higher, how steeply each rises, and where the lowest point of the curve sits.

How the smile shifts when price moves

When the underlying moves, does each strike keep its implied volatility, or does the whole curve slide along with the price? Traders describe two simple rules. Under sticky strike, each strike keeps its implied volatility, so as the price falls, the at-the-money point moves to a strike with higher volatility on the curve. Under sticky delta, the curve moves with the price, so an option with a given delta keeps the same implied volatility.

Real markets sit somewhere between the two and change behaviour with conditions. In sharp equity selloffs, at-the-money volatility usually rises faster than either rule would suggest. The choice of rule matters to anyone hedging options, because it changes how much delta an option really has.

It also affects dealer positioning estimates. A gamma map built by re-pricing the book at hypothetical prices has to assume how the smile moves, and different assumptions produce different results.

Reading the smile in practice

The lowest point of the smile shows where the market thinks outcomes are most clustered. A smile whose bottom sits above the current price suggests the market sees more room for a modest rise than a modest fall, while still pricing larger tails on both sides.

The steepness of the wings shows how much the market is paying for tail outcomes. Steep wings mean expensive insurance against large moves; flat wings mean the market is calm about the tails. Comparing the wings with their own history is more informative than comparing them with any fixed number.

Changes in the smile around events are especially telling. Before an earnings report or a binary decision, the wings often rise and the curve becomes more symmetric. After the event, both the overall level and the wings usually fall back.

Smiles before binary events

Single stocks facing an outcome that could send them sharply higher or lower, such as a regulatory ruling, a trial result or a takeover vote, often show a pronounced smile in the expiry that spans the event. Both wings are bid because both tails are plausible, and the curve can even develop two humps if the market expects the stock to land in one of two distinct price zones.

After the event the smile usually collapses toward a flatter, more ordinary shape, because the outcome that justified those tails is known. Anyone holding options in the wings through the event is exposed to that collapse as well as to the result itself.