Capturing the volatility smile: parametric volatility models versus stochastic volatility models

Black-Scholes option pricing model (1973) assumes that all option prices on the same underlying asset with the same expiration date, but different exercise prices should have the same implied volatility. However, instead of a flat implied volatility structure, implied volatility (inverting the Black-Scholes formula) shows a smile shape across strikes and time to maturity. This paper compares parametric volatility models with stochastic volatility models in capturing this volatility smile. Results show empirical evidence in favor of parametric volatility models.

Keywords: smile volatility, parametric, stochastic, Black-Scholes.
JEL Classification: C14 C68 G12 G13