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Multifractality in Asset Returns: Theory and Evidence

Author

Listed:
  • Laurent-Emmanuel Calvet

    () (Department of Economics, Harvard University - University of Harvard)

  • Adlai J. Fisher

    (Faculty of Commerce, University of British Columbia - University of British Columbia)

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.

Suggested Citation

  • Laurent-Emmanuel Calvet & Adlai J. Fisher, 2002. "Multifractality in Asset Returns: Theory and Evidence," Post-Print hal-00478175, HAL.
  • Handle: RePEc:hal:journl:hal-00478175
    DOI: 10.1162/003465302320259420
    Note: View the original document on HAL open archive server: https://hal-hec.archives-ouvertes.fr/hal-00478175
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