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Multifractality in Asset Returns: Theory and Evidence

Listed author(s):
  • 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)

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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Paper provided by HAL in its series Post-Print with number hal-00478175.

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Date of creation: Aug 2002
Publication status: Published in The Review of Economics and Statistics, 2002, Vol.84,n°3, pp.381-406. <10.1162/003465302320259420>
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
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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