Multifractal Financial Chaos in an Artificial Economy

Abstract

A model is proposed of a population of competing companies that are in a coevolutionary race and whose evolutionary performance is evaluated by a financial market, composed of value investors and of a breed of arbitrageurs that perform bargain arbitrage, trying to identify 'bargains' in the form of relative misspricings and, acting accordingly, buying assets with higher value at lower prices and selling assets with lower value at higher prices.

The model's equations are based on coupled networks of nonlinear maps, in this way, the model is focused on a coevolutionary process between companies and financial market. It is shown that, for a wide range of dynamical couplings and parameters, Multifractal Self-organized Criticality (MSOC) takes place, with the emergence of patterns of turbulence that closely resemble actual financial turbulence. The relation between arbitrage and multifractal financial turbulence is addressed.

Keywords: Multifractal chaos, financial turbulence, multifractal self-organized criticality, evolutionary arbitrage theory, financial markets’ efficiency, tail risk, evolutionary finance, microscopic financial modeling

JEL Classification: G1, G12, G14, C73, C6, C63