Passive motion in dynamical disorder as a model for stock market prices

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. Assuming a power-law decay of the time correlation of the disorder, the returns correlation decays rapidly but the correlation function of the absolute returns exhibits a slow power-law decay. 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. Implied volatilities for options pricing are found by numerical simulation.