bs01 Motion in random fields - an application to stock market data

Motion in random fields - an application to stock market data

http://www3.ul.ie/gleesonj/Papers/xmarket_randomfield_singlescale_ver4.pdf

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.