What Is a ‘Volatility Smile’ and What Does It Suggest about the Black-Scholes Assumption?

A Volatility Smile is a pattern observed when plotting the Implied Volatility (IV) of options with the same expiration date against different strike prices. Instead of a flat line, as assumed by the Black-Scholes model, the plot often forms a 'smile' or 'skew,' showing that options far out-of-the-money or deep in-the-money have higher IV than at-the-money options.

This suggests that the market does not believe asset price changes are normally distributed, violating a core Black-Scholes assumption.