Self-organizing three-dimensional Ising model of financial markets.

Abstract

The three-dimensional Ising model in an external field is used as a mathematical model for price dynamics of financials market. The model allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the stylized facts of the financial markets. We obtain the price dynamics in terms of the strength of the field that reinforces the sensitivity of the agent's sentiment to external news. The exponent of long-tail cumulative probability density is determined and satisfies the inverse of the cubic law. Furthermore, the long range memory of the model is studied using different methods to determine the Hurst index of the model. The results obtained display that the model does serve as a mathematical model for financial markets.