In finance, the volatility smile is the pattern in which in- and out-of-the-money options are observed to have higher implied volatilities than at-the-money options. A graph of implied volatility vs. strike price for a given expiry will form a upturned curve similar to the shape of a smile. The pattern displays different characteristics for different markets and is believed to result from risk averse traders' valuations of the probability of extreme price movements in the underlying instrument. Equity options traded in American markets did not show a volatility smile before the Crash of 1987 but began showing one afterwards. The phenomenon is not fully understood, and modeling the volatility smile is an active area of research in quantitative finance.
A related concept is that of term structure of volatility, which describes how (implied) volatility differs for related options with different maturities. An implied volatility surface is a 3-D plot that plots volatility smile and term structure of volatility in a consolidated three-dimensional surface for all options on a given underlying.
Read more about Volatility Smile: Volatility Smiles and Implied Volatility, Implied Volatility and Historical Volatility, Term Structure of Volatility, Implied Volatility Surface, Evolution: Sticky, Modeling Volatility
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