Eur. Phys. J. B 55, 161-167 (2007)
https://doi.org/10.1140/epjb/e2006-00205-y

A nonextensive approach to the dynamics of financial observables

¹ 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

Corresponding authors: ^a sdqueiro@cbpf.br - ^b moyano@cbpf.br - ^c jeferson@cbpf.br - ^d tsallis@santafe.edu

Received: 31 January 2006
Revised: 22 March 2006
Published online: 1 June 2006

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 . 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.