  In the Black-Scholes context we consider the probability distribution
function (PDF) of financial returns implied by volatility smile and we study
the relation between the decay of its tails and the fitting parameters of the
smile. We show that, considering a scaling law derived from data, it is
possible to get a new fitting procedure of the volatility smile that considers
also the exponential decay of the real PDF of returns observed in the financial
markets. Our study finds application in the Risk Management activities where
the tails characterization of financial returns PDF has a central role for the
risk estimation.
