Modelling financial time series using multifractal random walks

Multifractal random walks (MRW) correspond to simple solvable “stochastic volatility” processes. Moreover, they provide a simple interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that they are able to reproduce most of the recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics.