Volatility Skew vs Volatility Smile

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

Volatility skew and a volatility smile describe the same plot at different levels of generality. Solve every option price in one expiration for its implied volatility and plot the results against strike, moneyness, or delta. Volatility skew is the name for the fact that the resulting curve is not flat. A volatility smile is one particular shape that curve can take: a U, with both the low-strike and high-strike wings implying more volatility than the near-the-money center.

That makes the relationship one of category and member. A smile is a kind of skew. A downside smirk, where implied volatility climbs steeply as strikes fall and flattens as they rise, is also a kind of skew but is not a smile. A flat curve is the degenerate case that a single-volatility model would assume. Using skew as a catch-all is common in trading desks and vendor screens, so name the shape explicitly.

Both concepts belong to a single expiration. Stack many strike curves across maturities and you have a volatility surface. Compare only at-the-money implied volatility across those maturities and you have term structure. Traders sometimes say skew when they mean term structure, which mixes the horizontal and vertical dimensions of the surface and produces confused comparisons.

How volatility skew and smile are measured

Because they describe different features, they are measured with different arithmetic on the same data.

Skew is usually reported as asymmetry between matched points. A standard convention is 25-delta put implied volatility minus 25-delta call implied volatility for one expiration. Consider a 45-day expiration where the 25-delta put prints 31%, the at-the-money option prints 26%, and the 25-delta call prints 24%. Skew under that convention is 31% minus 24%, or 7 volatility points, with the put carrying a 5-point premium over the at-the-money level and the call sitting 2 points below it. That is textbook downside skew.

Smile is usually reported as curvature. Average the two matched wings and subtract the center. Consider a different 45-day chain where the 90 strike prints 28%, the 100 at-the-money strike prints 20%, and the 110 strike prints 27%. Average wing implied volatility is 27.5%, so curvature is 7.5 volatility points, while wing asymmetry is only 28% minus 27%, or 1 point. Both wings are materially above the center and close to each other, which is a broadly symmetric smile.

Run both diagnostics on both chains and the distinction becomes concrete. The first chain has 7 points of asymmetry but only 1.5 points of curvature, because averaging 31% and 24% gives 27.5% against a 26% center. The second has 7.5 points of curvature and 1 point of asymmetry. Same two numbers per chain, opposite readings, because curvature and asymmetry are independent features of one curve.

Measure both in moneyness or delta: ten dollars of strike is a different distance for a $50 stock and a $500 stock. Forward moneyness normalizes by the forward price, and matched absolute deltas compare similar tail locations, with delta itself moving with the model and implied volatility. Check the vendor’s sign convention before reading a risk reversal, since the convention differs across desks.

How traders use skew and smile readings

Read asymmetry when your position has legs on opposite sides of the chain or on one side only. A collar buys relatively expensive downside protection and sells a cheaper upside call, so the skew number is close to the trade’s economics. A risk reversal trades the put-call implied volatility difference directly, and it carries net delta even when the premiums offset. A vertical spread’s cost depends on where each of its two strikes sits on the curve, which is why two spreads of equal width can price very differently.

Read curvature when your position is long or short both wings. A long strangle pays for both tails, so an at-the-money implied volatility quote can badly understate the entry cost when curvature is high. A butterfly or condor is explicitly a curvature trade, buying the center against the wings or the reverse. The payoff and Greek exposures decide whether a structure is long or short the smile, not the name of the pattern on the screen.

Both readings feed the same risk work. A portfolio can show modest net vega and still carry large exposure to the curve steepening or flattening, because long and short legs sit at different strikes. A single parallel implied volatility shock misses that, so scenario analysis shocks the level, the curvature, and the asymmetry separately. Cross-Greeks such as vanna capture how delta and vega move together when spot and the surface shift.

The distinction also shows up at the index level. Cboe has described how skew drives the gap between the VIX Index, which is a variance calculation weighted across out-of-the-money strikes, and at-the-money implied volatility. When skew is zero the two are equal, and as skew steepens the spread widens. That is a direct consequence of the shape of the strike curve, not of the volatility level.

Data quality in skew and smile measurements

Price a wing from the quote you can trade. In a low-priced option, a few cents of price change moves solved implied volatility sharply, so check the bid and ask behind a dramatic wing before trading its midpoint. Bid, ask, midpoint, last trade, and fitted surface values differ on an illiquid chain, so read the shape from one source.

Put-call parity is a useful check at each strike. For European-style options, calls and puts at the same strike and expiration should imply a coherent forward once rates and dividends are handled. A large same-strike implied volatility gap usually points to stale quotes or bad inputs rather than tradable structure. Surface builders commonly use out-of-the-money puts below the forward and out-of-the-money calls above it for exactly this reason.

Options flow shows the curve move first. When aggressive buying hits one wing, it reprices that side of the curve before at-the-money implied volatility moves at all, which changes asymmetry without changing the headline number a trader is watching.

Bottom line

Skew is the category and smile is one member of it. Measure asymmetry with matched-delta put minus call implied volatility, measure curvature with average wing implied volatility minus the center, and report both, because one curve carries both features. Read asymmetry for collars, risk reversals and verticals, and curvature for strangles, butterflies and condors.