Scaling and multiscaling in financial series: a simple model

We propose a simple stochastic volatility model which is analytically tractable, very easy to simulate and which captures some relevant stylized facts of nancial assets, including scaling properties. In particular, the model displays a crossover in the log-return distribution from power-law tails (small time) to a Gaussian behavior (large time), slow decay in the volatility autocorrelation and multiscaling of moments. Despite its few param- eters, the model is able to t several key features of the time series of nancial indexes, such as the Dow Jones Industrial Average, with a remarkable accuracy.