VolatilitySmile - crowlogic/arb4j GitHub Wiki

A volatility smile is a pattern observed in the implied volatility of options across different strike prices, where the implied volatility appears to be higher for options that are deep in-the-money (ITM) or deep out-of-the-money (OTM), compared to at-the-money (ATM) options. This pattern is called a "smile" because when plotted on a graph, the implied volatilities form a curve resembling a smile.

The volatility smile contradicts the assumptions of the Black-Scholes option pricing model, which assumes that implied volatility is constant across all strike prices and maturities. The presence of a volatility smile suggests that the market perceives different levels of risk for ITM, ATM, and OTM options.