Financial market dynamics

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. (C) 2002 Elsevier Science B.V. All rights reserved.