A Multifractal Model of Asset Returns
Laurent Calvet (),
Benoît Mandelbrot and
Adlai J. Fisher
Working Papers from HAL
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: Multifractal model of asset returns; compund stochastic process; self-affinity; multiscaling; scaling laws; self-similarity; subordinated stochastic process; time deformation; trading time (search for similar items in EconPapers)
Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00601870
References: Add references at CitEc
Citations: Track citations by RSS feed
Published in 2011
There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.
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)
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 ().