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

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

2002-04-11

arxiv.org/abs/cond-mat/0204261v2

Physics

Condensed Matter

Statistical Mechanics

9 pages. Revised version, added derivation, deleted time homogeneous process. Submitted to Physica A

Scientific paper

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.

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