A Thermodynamic Picture of Financial Market and Model Risk

TL;DR

This paper models financial markets using thermodynamics, linking economic quantities to thermodynamic variables, and offers a novel framework for understanding and evaluating model risk through equilibrium and non-equilibrium thermodynamic principles.

Contribution

It introduces a thermodynamic framework for financial market analysis, providing new derivations and characterizations of worst-case risk using thermodynamic concepts.

Findings

Establishes a correspondence between thermodynamic and economic variables.

Derives characterization rules for worst-case risk using thermodynamics.

Provides Lagrangian and Hamiltonian formulations for risk assessment.

Abstract

By treating the financial market as a thermodynamic system, we establish a one-to-one correspondence between thermodynamic variables and economic quantities. Measured by the expected loss under the worst-case scenario, financial risk caused by model uncertainty is regarded as a result of the interaction between financial market and external information sources. This forms a thermodynamic picture in which a closed system interacts with an external reservoir, reaching its equilibrium at the worst-case scenario. The severity of the worst-case scenario depends on the rate of heat dissipation, caused by information sources reducing the entropy of the system. This thermodynamic picture leads to simple and natural derivation of the characterization rules of the worst-case risk, and gives its Lagrangian and Hamiltonian forms. With its help financial practitioners may evaluate risks utilizing both equilibrium and non-equilibrium thermodynamics.