"One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface … (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the … Dumas et al. (1998). In the second-stage we model the dynamics of the cross-sectional first-stage implied volatility surface …

"We analyze the volatility surface vs. moneyness and time to expiration implied by MIBO options written on the MIB30 …, the most important Italian stock index. We specify and fit a number of models of the implied volatility surface and find … that it has a rich and interesting structure that strongly departs from a constant volatility, Black-Scholes benchmark …