Continuous cascade models for asset returns

In this paper, we make a short overview of continuous cascade models recently introduced to model asset return fluctuations. We show that these models account in a very parcimonious manner for most of “stylized facts” of financial time series. We review in more details the simplest of such models namely the log-normal Multifractal Random Walk. It can simply be considered as a stochastic volatility model where the (log-) volatility memory has a peculiar ”logarithmic” shape. This model possesses some appealing stability properties with respect to time aggregation. We describe how one can estimate it using a GMM method and we present some applications to volatility and VaR forecasting.