Power law distributions and dynamic behaviour of stock markets
Department of Physics, Trinity College, Dublin 2, Ireland
Corresponding author: a firstname.lastname@example.org
Published online: 15 April 2001
A simple agent model is introduced by analogy with the mean field approach to the Ising model for a magnetic system. Our model is characterised by a generalised Langevin equation where is the usual Gaussian white noise, i.e.: and . Both the associated Fokker Planck equation and the long time probability distribution function can be obtained analytically. A steady state solution may be expressed as where and Z is a normalization factor. This is explored for the simple case where and fluctuations characterised by the amplitude when it readily yields for , a distribution function with power law tails, viz: . The parameter c ensures convergence of the distribution function for large values of φ. It might be loosely associated with the activity of so-called value traders. The parameter J may be associated with the activity of noise traders. Output for the associated time series show all the characteristics of familiar financial time series providing J< 0 and .
PACS: 05.10.Gg – Stochastic analysis methods (Fokker-Planck, Langevin, etc.) / 89.65.Gh – Economics, business, and financial markets
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001