This anomaly implies deficiencies in the standard Black–Scholes option pricing model which assumes constant volatility and log-normal distributions of underlying asset returns.
It is believed that investor reassessments of the probabilities of fat-tail have led to higher prices for out-of-the-money options. Equity options traded in American markets did not show a volatility smile before the Crash of 1987 but began showing one afterwards. The pattern differs across various markets. Graphing implied volatilities against strike prices for a given expiry produces a skewed 'smile' instead of the expected flat surface. These options are said to be either deep in-the-money or out-of-the-money. In particular for a given expiration, options whose strike price differs substantially from the underlying asset's price command higher prices (and thus implied volatilities) than what is suggested by standard option pricing models. It is a parameter (implied volatility) that is needed to be modified for the Black–Scholes formula to fit market prices. Volatility smiles are implied volatility patterns that arise in pricing financial options.
