Skip to Main content Skip to Navigation
Journal articles

Multifractality in Asset Returns: Theory and Evidence

Abstract : This paper investigates the multifractal model of asset returns (MMAR), a class of continuous-time processes that incorporate the thick tails and volatility persistence exhibited by many financial time series. The simplest version of the MMAR compounds a Brownian motion with a multifractal time-deformation. Prices follow a semi-martingale, which precludes arbitrage in a standard two-asset economy. Volatility has long memory, and the highest finite moments of returns can take any value greater than 2. The local variability of a sample path is highly heterogeneous and is usefully characterized by the local Hölder exponent at every instant. In contrast with earlier processes, this exponent takes a continuum of values in any time interval. The MMAR predicts that the moments of returns vary as a power law of the time horizon. We confirm this property for Deutsche mark/U.S. dollar exchange rates and several equity series. We develop an estimation procedure and infer a parsimonious generating mechanism for the exchange rate. In Monte Carlo simulations, the estimated multifractal process replicates the scaling properties of the data and compares favorably with some alternative specifications.
Document type :
Journal articles
Complete list of metadatas
Contributor : Antoine Haldemann <>
Submitted on : Friday, April 30, 2010 - 2:21:25 PM
Last modification on : Friday, December 18, 2020 - 5:30:02 PM




Laurent-Emmanuel Calvet, Adlai J. Fisher. Multifractality in Asset Returns: Theory and Evidence. Review of Economics and Statistics, Massachusetts Institute of Technology Press (MIT Press), 2002, Vol.84,n°3, pp.381-406. ⟨10.1162/003465302320259420⟩. ⟨hal-00478175⟩



Record views