Continuous cascade models for asset returns

Abstract

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 continuous cascade namely the log-normal multifractal random walk (MRW). 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) Value at Risk forecasting.