This paper describes the implied volatility function computed from options on the Italian stock market index between 1995 and 1998 and tries to find out potential explanatory variables. We find that the typical smirk observed for S&P500 stock index characterizes also Mib30 stock index. When potential determinants are investigated by a linear Granger Causality test, the important role played by option's time to expiration, transacted volumes and historical volatility is detected. A possible proxy of portfolio insurance activity does poorly in explaining the observed pattern. Further analysis shows that the dynamic interrelation between the implied volatility function and some determinants could be, to a certain extent, non-linear.