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The Dynamics of Financial Markets -- Mandelbrot's multifractal cascades, and beyond

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Author Info
Lisa Borland (Evnine-Vaughan Associates, Inc.)
Jean-Philippe Bouchaud (Science & Finance, Capital Fund Management, CEA Saclay;)
Jean-Francois Muzy (Centre de Recherche Paul Pascal, Pessac, FRANCE)
Gilles Zumbach (Consulting in Financial Research)
Abstract

This is a short review in honor of B. Mandelbrot's 80st birthday, to appear in W ilmott magazine. We discuss how multiplicative cascades and related multifractal ideas might be relevant to model the main statistical features of financial time series, in particular the intermittent, long-memory nature of the volatility. We describe in details the Bacry-Muzy-Delour multifractal random walk. We point out some inadequacies of the current models, in particular concerning time reversal symmetry, and propose an alternative family of multi-timescale models, intermediate between GARCH models and multifractal models, that seem quite promising.

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Paper provided by Science & Finance, Capital Fund Management in its series Science & Finance (CFM) working paper archive with number 500061.

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Date of creation: Jan 2005
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Handle: RePEc:sfi:sfiwpa:500061

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G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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  1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 14(1), pages 113-47.
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  3. Jean-Philippe Bouchaud & Marc Potters & Martin Meyer, 1999. "Apparent multifractality in financial time series," Science & Finance (CFM) working paper archive 9906347, Science & Finance, Capital Fund Management. [Downloadable!]
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  10. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August. [Downloadable!] (restricted)
  11. Benoit Pochard & Jean-Philippe Bouchaud, 2002. "The skewed multifractal random walk with applications to option smiles," Science & Finance (CFM) working paper archive 0204047, Science & Finance, Capital Fund Management. [Downloadable!]
  12. Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July. [Downloadable!] (restricted)
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