A stochastic model for multifractal behaviour of stock prices

We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a Markovian stochastic process which is able to reproduce the experimentally observed volatility clustering and fat tails in the probability density functions (PDF) of financial time series. More importantly, the process also reproduces the PDF time scaling, the power law memory of volatility and the apparent multifractality of the time series up to the time scale which is experimentally observable.