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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.
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Submitted on : Friday, April 30, 2010 - 2:21:25 PM
Last modification on : Thursday, March 26, 2020 - 4:39:25 PM

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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⟩

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