Scaling in Different Dynamic Regimes of a Multi-agent Stock Market Model

Approaches of both theoretical analysis and computer simulation are used to study a stochastic multi-agent stock market model. Theoretical analysis provides the parameter settings for different dynamic regimes including fundamental equilibrium, non-fundamental equilibrium, periodicity and chaos. Agent-based computer simulations with those settings are performed to produce the price series. Statistical analysis of these data shows: markets of all regimes present power law scaling of the return distribution and temporal dependence in volatility; the fundamental equilibrium regime has the largest scaling exponent a of the Pareto distribution for return and smallest self-similarity exponent H of temporal dependence in volatility, and non-fundamental equilibrium regime has the smallest a and largest H, with periodicity and chaos regimes in between.