A nonextensive approach to the dynamics of financial observables
Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil
2 Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico, 87501, USA
Revised: 22 March 2006
Published online: 1 June 2006
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 . 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 qstat+qsens=2 is numerically satisfied, qstat and qsens 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.
PACS: 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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006