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Continuous-Time Skewed Multifractal Processes as a Model for Financial Returns

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  04 February 2016

Emmanuel Bacry ,
Laurent Duvernet  and
Jean-François Muzy
Emmanuel Bacry*
Affiliation:
CNRS and École Polytechnique
Laurent Duvernet*
Affiliation:
Université Paris-Est Marne-la-Vallée and École Polytechnique
Jean-François Muzy*
Affiliation:
CNRS, Université de Corse, and École Polytechnique
*
∗ Postal address: Centre de Mathématiques Appliquées UMR 7641, École Polytechnique CNRS, Route de Saclay, 91128 Palaiseau Cedex, France. Email address: emmanuel.bacry@polytechnique.fr
∗∗ Postal address: Laboratoire MODAL‘X, Département de Mathématiques, UFR SEGMI, Université Paris Ouest-Nanterre, 200 avenue de la République, 92001 Nanterre Cedex, France. Email address: duvernet@cmap.polytechnique.fr
∗∗∗ Postal address: Laboratoire SPE UMR 6134, Université de Corse CNRS, 20250 Corte, France. Email address: muzy@univ-corse.fr
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Abstract

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We present the construction of a continuous-time stochastic process which has moments that satisfy an exact scaling relation, including odd-order moments. It is based on a natural extension of the multifractal random walk construction described in Bacry and Muzy (2003). This allows us to propose a continuous-time model for the price of a financial asset that reflects most major stylized facts observed on real data, including asymmetry and multifractal scaling.

Keywords

Multifractal processskewnessleverage effect

MSC classification

Primary: 91B25: Asset pricing models 91B24: Price theory and market structure 60G18: Self-similar processes
Type
Research Article
Information
Journal of Applied Probability , Volume 49 , Issue 2 , June 2012 , pp. 482 - 502
Copyright
© Applied Probability Trust 

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