Information thermodynamics of financial markets: the Glosten-Milgrom model

TL;DR

This paper draws an analogy between the Glosten-Milgrom financial market model and Szilard's information engine, revealing how thermodynamic concepts can describe market dynamics and inform bounds on trader gains.

Contribution

It introduces a novel analogy linking financial market strategies to thermodynamic work extraction, providing a new perspective on market efficiency and information use.

Findings

Optimal market maker strategy matches work extraction protocols in thermodynamics.

Market temperature is derived from order distribution, analogous to physical temperature.

Informed traders' expected gains are bounded by market temperature and information amount.

Abstract

The Glosten-Milgrom model describes a single asset market, where informed traders interact with a market maker, in the presence of noise traders. We derive an analogy between this financial model and a Szil\'ard information engine by {\em i)} showing that the optimal work extraction protocol in the latter coincides with the pricing strategy of the market maker in the former and {\em ii)} defining a market analogue of the physical temperature from the analysis of the distribution of market orders. Then we show that the expected gain of informed traders is bounded above by the product of this market temperature with the amount of information that informed traders have, in exact analogy with the corresponding formula for the maximal expected amount of work that can be extracted from a cycle of the information engine. This suggests that recent ideas from information thermodynamics may shed light on financial markets, and lead to generalised inequalities, in the spirit of the extended second law of thermodynamics.