Statistical mechanics and financial markets: Antagony between derivatives and market self-regulation

Abstract

We establish specific correspondences between notions of economics and statistical mechanics. There are several situations wherein a rather accurate correspondence has already been established, for instance in utility theory for exchange economy with quasilinear utility function, which has been mapped to analogous thermodynamics. We discuss how statistical mechanics can be applied to define the efficiency of financial markets, via a mapping of stock fluctuations to the Random Energy Model (REM) at particular temperatures. We introduce the concept of reflection in economics; the effective reflection number, in particular, is found to be crucial in understanding the self-regulation of the market. We also establish a qualitative similarity between market with derivatives and certain statistical mechanics models. Such an analogy supports a hypothesis that financial derivatives are antagonistic to the self-regulation of financial markets. As a whole, our analysis is complementary to established concepts and methods of neoclassical economics for markets without derivatives.