An Exact Physical Approach to Market Participation Models

Some new approaches to macroeconomic modeling describe macroscopic variables in terms of the behavior of a large collection of microeconomic entities; we give an exact model able to unify a large number of hypotheses introduced in this approach. Our treatise starts from the best known discrete model of classical Statistical Physics, the Ehrenfest urn model. The main generalization we perform consists in introducing “choice correlations” between agents, that give rise to “herd behavior” if they are strong and positive. These processes are homogeneous Markov chains whose transition matrix is determined by a parameter vector describing probabilities and correlation in state changes. The model is exactly soluble for most interesting cases. From applications to the clustering of agents the Ewens Sampling Formula is derived in an exact simple way, as a limiting case of our chain. Applications to stock price dynamics are shown. High positive correlation between market participants explicates the large observed values of kurtosis of the price increments.