Volatility Smile and Skew

If the Black Scholes model were exactly right, every option on the same underlying and expiry would trade at the same implied volatility. In reality, implied volatility varies by strike. Plotted against strike, it often forms a "smile", higher at both ends, or a "skew" (also called a smirk), higher on one side. These shapes reveal how the market prices crash risk, rally risk and fat tails, and they matter for every option strategy that uses more than one strike.

Typical shapes by market#

Why skew exists#

• Fat tails: real returns have more extreme moves than the lognormal distribution assumes, especially on the downside for stocks. Higher IV on far strikes corrects for this. See Fat Tails.
• Crash memory: the steep equity skew became a lasting feature after the October 1987 crash. See Black Monday 1987.
• Volatility rises when prices fall: for equities, falling prices usually bring higher volatility, so low strikes are priced with higher volatility.
• Supply and demand: investors buy index puts for protection and sell calls for income (covered calls), pushing put IV up and call IV down.
• Leverage effect: as stock prices fall, companies become more leveraged and riskier.

Measuring skew#

Skew and strategy#

See Collars, Bear Put Spread and Skew Trading.

Sticky strike vs sticky delta#

When the underlying moves, how does the smile move?

• Sticky strike: each strike keeps its implied volatility; at the money volatility changes as the price moves along the skew.
• Sticky delta (sticky moneyness): the smile moves with the price, so options at the same moneyness keep the same volatility.

Real markets fall somewhere in between and vary by regime. The assumption changes deltas and hedges, which is why models like SABR and local volatility differ. See Volatility Surface Dynamics.

Common mistakes#

• Assuming all strikes have the same IV.
• Judging an option as cheap or expensive by comparing its IV with at the money IV without accounting for normal skew.
• Forgetting skew changes with market stress.

Frequently asked questions#

What is the volatility smile?#

The pattern in which implied volatility is higher for options far from the current price than for at the money options, forming a curve shaped like a smile.

Why do index puts have higher implied volatility?#

Because of crash risk, strong demand for portfolio protection and the tendency for volatility to rise when stock prices fall.

What is a risk reversal in volatility terms?#

The difference between the implied volatility of an out of the money call and an equally out of the money put, often at 25 delta, used to measure skew.

Next, see how smiles across expiries form the Volatility Surface.