Narrow Results

In Ref. 1, a new model for the description of the financial markets dynamics has been proposed. Traders move on a two dimensional lattice and interact by means of mechanisms of mutual influence. In the present paper, we present results from large-scale simulations of the same model enhanced by the introduction of rational traders modeled as moving-averages followers. The dynamics now accounts for log-normal distribution of volatility which is consistent with some observation of real financial indexes⁷ at least for the central part of the distribution.

Lattice-based models have been attracting much interest in recent years and have been applied to many complex systems. The derivation of large scale dynamical equations of lattice-gas models as well as lattice-Boltzmann models was based on the belief that only the physically interesting quantities (mass, momentum and energy) are conserved. Staggered invariants in lattice-gas models were found in 1988 and there have been no efficient methods to eliminate these invariants. In this paper, we will first discuss the existence of staggered invariants, then we propose to use fractional propagation as an effective way of suppressing these undesired invariants. Numerical simulations will be used to confirm the theory and to show the improvement of computations.