Black-Scholes-Like Derivative Pricing With Tsallis Non-extensive Statistics

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dc.creatorMichael, Fredrick
dc.creatorJohnson, M. D.
dc.date2002-04-11
dc.date2002-04-30
dc.date.accessioned2026-07-07T12:06:40Z
dc.date.available2026-07-07T12:06:40Z
dc.descriptionWe 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.
dc.description9 pages. Revised version, added derivation, deleted time homogeneous process. Submitted to Physica A
dc.identifierhttps://arxiv.org/abs/cond-mat/0204261
dc.identifierhttp://arxiv.org/abs/cond-mat/0204261
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208722
dc.subjectStatistical Mechanics
dc.subjectDisordered Systems and Neural Networks
dc.subjectPricing of Securities
dc.titleBlack-Scholes-Like Derivative Pricing With Tsallis Non-extensive Statistics
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