Truncated Levy distribution of SP500 stock index fluctuations. Distribution of one-share fluctuations in a model space

Truncated Levy distributions of “SP500” stock index fluctuations (Mantegna, Stanley, Nature 376 (1995) 46) are obtained in the formerly introduced model (Romanovsky, Physica A 265 (1999) 264) for stock market. A one-body random kinematics in this space corresponds to the one-shares fluctuations on stock exchange. The statistics of such kinematics is investigated, and the asymptotic distribution of one-share fluctuations was obtained. All results are compared with the known “experimental” data (Mantegna, Stanley, Nature 376 (1995) 46; Plerou et al., Phys. Rev. E 60 (1999) 6519 and 5306; Gopikrishnan et al., Eur. J. Phys. B (1998) 138).