Modelling fluctuations of financial time series: from cascade process to   stochastic volatility model
  In this paper, we provide a simple, ``generic'' interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as observed recently by Bonanno et al., naturally emerge. We then propose a simple solvable ``stochastic volatility'' model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided. 
J.F. Muzy (1), J. Delour (1) and E. Bacry (2) ((1) CRPP-CNRS Pessac   France, (2) CMAP Ecole Polytecnhique Palaiseau France)