Financial market dynamics

Abstract

A necessary precondition for modeling financial markets is a complete understanding of their statistics, including dynamics. Distributions derived from nonextensive Tsallis statistics are closely connected with dynamics described by a nonlinear Fokker–Planck equation. The combination shows promise in describing stochastic processes with power-law distributions and superdiffusive dynamics. We investigate intra-day price changes in the S& P500 stock index within this framework. We find that the power-law tails of the distributions, and the index's anomalously diffusing dynamics, are very accurately described by this approach. Our results show good agreement between market data and Fokker–Planck dynamics. This approach may be applicable in any anomalously diffusing system in which the correlations in time can be accounted for by an Ito–Langevin process with a simple time-dependent diffusion coefficient.