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

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.

arXiv comment24 pages, to appear in Wilmott Magazine special issue for Mandelbrot

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Cited by in corpus (5)

• Hitting Time Distributions in Financial Markets
• The dynamics of financial stability in complex networks
• Characteristic Function of the Tsallis $q$-Gaussian and Its Applications in Measurement and Metrology
• A Dynamic Bayesian Model for Interpretable Decompositions of Market Behaviour
• Heavy-tails in economic data: fundamental assumptions, modelling and analysis