SVQ · Volatility surface
Volatility smile and skew
Also called: volatility smile, volatility skew, vol smirk
The volatility smile and skew describe how implied volatility varies with strike for a single expiry, revealing how the market prices tail moves.
Definition
For one expiry, plotting implied volatility against strike rarely gives a flat line. A smile is a curve that rises in both wings; a skew (or smirk) is a curve that slopes, typically with low strikes carrying higher implied volatility than high strikes.
Equity indices usually show a pronounced downside skew. Some commodities and currencies show more symmetric smiles or upside skew, depending on which direction the market fears.
Intuition
A flat line would mean the market believes returns are lognormal with constant volatility. The smile is the market saying otherwise: large moves happen more often than a normal distribution allows (fat tails), and in equities volatility tends to rise when prices fall.
Skew is therefore a price of asymmetric risk. Buyers of downside protection bid up out-of-the-money puts, and dealers who sell them demand compensation for the gap risk they carry.
How it's calculated
Common skew measures for one expiry:
- Risk reversal:
RR25 = σ(25Δ call) − σ(25Δ put). Negative values mean puts are priced richer than calls. - Butterfly (curvature):
BF25 = ½[σ(25Δ call) + σ(25Δ put)] − σ(ATM), a measure of how much the wings sit above the center. - Slope at the money:
∂σ / ∂kat k = 0, where k = ln(K/F).
Delta-based measures are preferred for comparisons across time and assets because a fixed strike drifts in moneyness as spot moves.
Example: with the 25-delta call at 17%, the 25-delta put at 23% and at-the-money at 18%, the risk reversal is −6 points and the butterfly is ½(17 + 23) − 18 = 2 points.
How to read it
Steepening downside skew means protection is getting more expensive relative to at-the-money options. Flattening means the premium for crash risk is easing. Rising curvature with stable skew points to demand for both wings, which is common before binary events.
Skew interacts with the level of volatility: in equities, skew often steepens as volatility rises. Compare skew against its own history for that asset and tenor rather than against a universal threshold.
Common mistakes
- Measuring skew at fixed strikes over time; spot moves change moneyness and create apparent skew changes that are only drift.
- Ignoring liquidity in the wings, where wide quotes can make skew look steeper or flatter than it really is.
- Reading skew as a forecast of direction. It prices the cost of protection, which is not the same as a probability of a fall.
- Comparing smiles across expiries without converting to a common scale such as delta or standardized moneyness.
In Saqrid
SVQ shows the smile in three dimensions on its rotatable implied-volatility surface, so skew can be read across every expiry at once.
A Crash-O-Meter reads put-skew crash fear per symbol, alongside the volatility risk premium.
Open SVQ.
Go deeper
Saqrid Institute lesson: Implied Volatility & the Smile. Lesson text is open to read without an account.