Motion in random fields - an application to stock market data

Details Motion in random fields - an application to stock market data Motion in random fields - an application to stock market data

2003-11-28

arxiv.org/abs/cond-mat/0311646v1

Physics

Condensed Matter

Statistical Mechanics

28 pages, 10 figures

Scientific paper

10.1117/12.556444

A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-scale field show characteristics similar to those found in empirical studies of stock market data. Specifically, short-term returns have a non-Gaussian distribution, with super-diffusive volatility, and a fast-decaying correlation function. The correlation function of the absolute value of returns decays as a power-law, and the returns distribution converges towards Gaussian over long times. Some important characteristics of empirical data are not, however, reproduced by the model, notably the scaling of tails of the cumulative distribution function of returns.

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