Financial Markets and the Phase Transition between Water and Steam

TL;DR

This paper models financial markets using a lattice gas analogy, linking market dynamics to phase transitions like water and steam, and predicts market auto-correlations and Hurst exponents through critical phenomena.

Contribution

It introduces a novel lattice gas model of financial markets based on the Ising model, connecting market behavior to critical phase transition theory.

Findings

Market auto-correlations can be explained by critical phenomena near phase transition.

A fractal network dimension close to 3 is consistent with empirical data.

Correlation times in markets can be as long as economic cycles.

Abstract

Motivated by empirical observations on the interplay of trends and reversion, a lattice gas model of financial markets is presented. The shares of an asset are modeled by gas molecules that are distributed across a hidden social network of investors. The model is equivalent to the Ising model on this network, whose magnetization represents the deviation of the asset price from its value. Moreover, the system should drive itself to its critical temperature in efficient markets. There, it is characterized by universal critical exponents, in analogy with the second-order phase transition between water and steam. These critical exponents imply predictions for the auto-correlations of financial market returns and for Hurst exponents. For a simple network topology, consistency with empirical observations implies a fractal network dimension near 3, and a correlation time at least as long as the economic cyle. To also explain the observed market auto-correlations at intermediate scales, the model should be extended beyond the critical domain, to other network topologies, and to other models of critical dynamics.