Define “Volatility Smile” and Its Implication for the Black-Scholes Model

The volatility smile is an empirical observation in the options market where options with the same expiration date but different strike prices have different implied volatilities. When implied volatility is plotted against the strike price, the resulting curve often forms a U-shape, or "smile." This observation directly contradicts the Black-Scholes model's core assumption that implied volatility is constant across all strike prices for a given expiration.

It implies that the market prices the risk of extreme movements (deep ITM or OTM) higher than the model predicts.