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.
Glossar
Implied Volatility
Expectation ⎊ This value represents the market's consensus forecast of future asset price fluctuation, derived by reversing option pricing models using current market premiums.
Volatility Smile
Curve ⎊ The volatility smile, observed in options markets, represents the graphical depiction of implied volatility across different strike prices for options with the same expiration date.
The Black-Scholes Model
Foundation ⎊ The Black-Scholes model serves as the cornerstone for modern options pricing theory, providing a continuous-time framework for calculating the fair value of derivatives.