2002/04/11 by Fredrick Michael, Michael D. Johnson, Michael, Fredrick +1
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 #Pricing of Securities (q-fin.PR) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy
paper · pdf · doi:10.48550/arxiv.cond-mat/0204261
openalex publication_date 2002/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We recently showed that the S&P500 stock market index is well described by Tsallis non-extensive statistics and nonlinear Fokker-Planck time evolution. We argued that these results should be applicable to a broad range of markets and exchanges where anomalous diffusion and `heavy' tails of the distribution are present. In the present work we examine how the Black-Scholes derivative pricing formula is modified when the underlying security obeys non-extensive statistics and Fokker-Planck time evolution. We answer this by recourse to the underlying microscopic Ito-Langevin stochastic differential equation of the non-extensive process.