A Multifractal Model of Asset Returns

Laurent Calvet, Benoît Mandelbrot and Adlai Fisher

Working Papers from HAL

Abstract: This paper presents the multifractal model of asset returns ("MMAR"), based upon the pioneering research into multifractal measures by Mandelbrot (1972, 1974). The multifractal model incorporates two elements of Mandelbrot's past research that are now well-known in finance. First, the MMAR contains long-tails, as in Mandelbrot (1963), which focused on Levy-stable distributions. In contrast to Mandelbrot (1963), this model does not necessarily imply infinite variance. Second. the model contains long-dependence, the characteristic feature of fractional Brownian Motion (FBM), introduced by Mandelbrot and van Ness (1968). In contrast to FBM, the multifractal model displays long dependence in the absolute value of price increments, while price increments themselves can be uncorrelated. As such, the MMAR is an alternative to ARCH-type representations that have been the focus of empirical research on the distribution of prices for the past fifteen years. The distinguishing feature of the multifractal model is multi-scaling of the return distribution's moments under time-rescalings. We define multiscaling, show how to generate processes with this property, and discuss how these processes differ from the standard processes of continuous-time finance. The multifractal model implies certain empirical regularities, which are investigated in a companion paper.

Keywords: self-affinity; Multifractal model of asset returns; compund stochastic process; subordinated stochastic process; time deformation; trading time; scaling laws; multiscaling; self-similarity (search for similar items in EconPapers)
Date: 2011-06-21
References: Add references at CitEc
Citations:

Published in 2011

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
Working Paper: A Multifractal Model of Assets Returns (1999)
Working Paper: A Multifractal Model of Asset Returns (1997)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-00601870

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().