Analogies between financial markets and critical phenomena have long been observed empirically. So far, no convincing theory has emerged that can explain these empirical observations. Here, we take a step towards such a theory by modeling financial markets as a lattice gas. The lattice represents the social network of investors, and the gas molecules represent the shares of an asset that are distributed across this network. In efficient markets, it is argued that arbitrageurs drive this lattice gas to its critical temperature, where it undergoes a second-order phase transition in analogy with that of water and steam. There, it is described by a renormalizable field theory and characterized by universal critical exponents. We show that this can replicate key features of the empirically observed scaling behavior of financial market returns. Working out these analogies with critical phenomena further should lead us to a new and deeper understanding not only of financial markets but of social networks in general.
Christof Schmidhuber received his Ph.D. in theoretical physics from CalTech in 1993 with a thesis on superstring theory under its founding father John H. Schwarz. He then worked as a postdoc at Princeton University and CERN, before switching to the hedge fund industry in 2001. After holding senior positions at Credit Suisse and other firms, Christof founded his own systematic asset manager and ran a UCITS fund with his team. While developing trading strategies, he noticed close analogies between financial markets and critical phenomena. In order to work them out and publish them, he returned to academia at Zurich University of Applied Sciences in 2018, where he is currently professor of financial mathematics and head of the group of finance, risk management, and econometrics.