A nonextensive approach to the dynamics of financial observables

S. M.D. Queirós (), L. G. Moyano (), J. de Souza () and C. Tsallis ()

The European Physical Journal B: Condensed Matter and Complex Systems, 2007, vol. 55, issue 2, 161-167

Abstract: We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy $S_{q}=k\frac{1-\sum_{i=1}^{W} p_{i} ^{q}}{1-q}\, (q\in \Re) \left(S_{1} \equiv S_{BG}=-k\sum_{i=1}^{W}p_{i}\,\ln p_{i}\right)$ . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q stat +q sens =2 is numerically satisfied, q stat and q sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Keywords: 05.90.+m Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems, 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion, 89.65.Gh Economics; econophysics, financial markets, business and management, (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations: View citations in EconPapers (12)

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DOI: 10.1140/epjb/e2006-00205-y

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