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

Lisa Borland, Jean-Philippe Bouchaud, Jean-Francois Muzy and Gilles Zumbach

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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.

Date: 2005-01
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