We examine how the Black–Scholes derivative pricing formula is modified when the underlying security obeys non-extensive statistics and Fokker–Planck dynamics. An unusual feature of such securities is that the volatility in the underlying Ito–Langevin equation depends implicitly on the...

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...