Continuous cascade models for asset returns

Emmanuel Bacry (), Alexey Kozhemyak and J.-F. Muzy ()
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Emmanuel Bacry: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
Alexey Kozhemyak: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique
J.-F. Muzy: SPE - Laboratoire « Sciences pour l’Environnement » (UMR CNRS 6134 SPE) - CNRS - Centre National de la Recherche Scientifique - Università di Corsica Pasquale Paoli [Université de Corse Pascal Paoli]

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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.

Date: 2008-01-01
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Citations: View citations in EconPapers (32)

Published in Journal of Economic Dynamics and Control, 2008, pp.156-199. ⟨10.1016/j.jedc.2007.01.024⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00604449

DOI: 10.1016/j.jedc.2007.01.024

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