Multifractality in Asset Returns: Theory and Evidence

Laurent Calvet and Adlai Fisher

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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.

Keywords: Multifractality; Asset returns; Theory and evidence (search for similar items in EconPapers)
Date: 2002-08
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Citations: View citations in EconPapers (149)

Published in Review of Economics and Statistics, 2002, Vol.84,n°3, pp.381-406. ⟨10.1162/003465302320259420⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00478175

DOI: 10.1162/003465302320259420

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