Volatility smile

In finance, the volatility smile is a long-observed pattern in which at-the-money options tend to have lower implied volatilities than other options. The pattern displays different characteristics for different markets, and is not well understood theoretically. In particular, American equity options did not show a volatility smile before the Crash of 1987 but began showing one afterwards.

A closely related concept is that of term structure of volatility, which refers to how implied volatility differs for related options with different maturities. An implied volatility surface is a 3-D plot that combines volatility smile and term structure of volatility into a consolidated view of all options for an underlier.

Source: Wikipedia