2001/08/01 by Fredrick Michael, Michael D. Johnson, Michael, Fredrick +1 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Economics and business #FOS: Physical sciences #Financial Risk and Volatility Modeling #Statistical Finance (q-fin.ST) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.cond-mat/0108017
openalex publication_date 2001/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Distributions derived from non-extensive 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 by direct analysis and by simulation. 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, Fokker-Planck dynamics, and simulation. Thus the combination of the Tsallis non-extensive entropy and the nonlinear Fokker-Planck equation unites in a very natural way the power-law tails of the distributions and their superdiffusive dynamics.