  In this work we afford the statistical characterization of a linear
Stochastic Volatility Model featuring Inverse Gamma stationary distribution for
the instantaneous volatility. We detail the derivation of the moments of the
return distribution, revealing the role of the Inverse Gamma law in the
emergence of fat tails, and of the relevant correlation functions. We also
propose a systematic methodology for estimating the parameters, and we describe
the empirical analysis of the Standard & Poor 500 index daily returns,
confirming the ability of the model to capture many of the established stylized
fact as well as the scaling properties of empirical distributions over
different time horizons.
