Financial Markets and the Phase Transition between Water and Steam
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. It is argued that the system is driven to its critical temperature in efficient markets. There, it is characterized by universal critical exponents, in analogy with the secondorder phase transition between water and steam. These critical exponents imply predictions for the autocorrelations of financial market returns. For a simple network topology, consistency with the observed longterm autocorrelations implies a fractal network dimension of 3.3, and a correlation time of 10 years. To also explain the observed shortterm autocorrelations, the model should be extended beyond the critical domain, to other network topologies, and to other models of critical dynamics.
 Publication:

arXiv eprints
 Pub Date:
 July 2021
 arXiv:
 arXiv:2107.03857
 Bibcode:
 2021arXiv210703857S
 Keywords:

 Quantitative Finance  Statistical Finance;
 High Energy Physics  Theory;
 Nonlinear Sciences  Cellular Automata and Lattice Gases;
 Physics  Physics and Society;
 Quantitative Finance  General Finance
 EPrint:
 34 pages, 7 figures