Definition of 'Volatility Smile'
A common graphical shape that results from plotting the strike price and implied volatility of a group of options with the same expiration date. The volatility smile is so named because it looks like a person smiling. The implied volatility is derived from the Black-Scholes model, and the volatility adjusts according to the option’s maturity and the extent to which it is in-the-money (moneyness).
Investopedia explains 'Volatility Smile'
Changes in an option’s strike price affect whether the option is in-the-money or out-of-the-money. The more an option is in-the-money or out-of-the-money, the greater its implied volatility becomes. The relationship between an option’s implied volatility and strike price can be seen in the graph below.
The volatility smile was first seen after the 1987 stock market crash, and was not present before. This may be the result in changes in investor behavior, such as a fear of another crash or black swan, as well as structural issues that go against Black-Scholes option pricing assumptions.