'Quantum Equilibrium-Disequilibrium': Asset Price Dynamics, Symmetry Breaking, and Defaults as Dissipative Instantons

51 Pages Posted: 15 Aug 2018 Last revised: 29 May 2019

See all articles by Igor Halperin

Igor Halperin

Fidelity Investments, Inc.

Matthew Francis Dixon

Illinois Institute of Technology - Stuart School of Business, IIT

Date Written: May 27, 2019

Abstract

We propose a simple non-equilibrium model of a financial market as an open system with a possible exchange of money with an outside world and market frictions (trade impacts) incorporated into asset price dynamics via a feedback mechanism. Using a linear market impact model, this produces a non-linear two-parametric extension of the classical Geometric Brownian Motion (GBM) model, that we call the ”Quantum Equilibrium-Disequilibrium” (QED) model. The QED model gives rise to non-linear mean-reverting dynamics, broken scale invariance, and corporate defaults. In the simplest one-stock (1D) formulation, our parsimonious model has only one degree of freedom, yet calibrates to both equity returns and credit default swap spreads. Defaults and market crashes are associated with dissipative tunneling events, and correspond to instanton (saddle-point) solutions of the model. When market frictions and inflows/outflows of money are neglected altogether, ”classical” GBM scale-invariant dynamics with an exponential asset growth and without defaults are formally recovered from the QED dynamics. However, we argue that this is only a formal mathematical limit, and in reality the GBM limit is non- analytic due to non-linear effects that produce both defaults and divergence of perturbation theory in a small market friction parameter.

Keywords: Geometric Brownian Motion, Financial Markets, Non-Equilibrium, Physics, Phase Transitions, Supersymmetry

JEL Classification: G00, G01, G11, G12, G14, G19, C50, C51, C52, C60, C61, C62, C65, C68

Suggested Citation

Halperin, Igor and Dixon, Matthew Francis, 'Quantum Equilibrium-Disequilibrium': Asset Price Dynamics, Symmetry Breaking, and Defaults as Dissipative Instantons (May 27, 2019). Available at SSRN: https://ssrn.com/abstract=3223243 or http://dx.doi.org/10.2139/ssrn.3223243

Igor Halperin (Contact Author)

Fidelity Investments, Inc. ( email )

United States

Matthew Francis Dixon

Illinois Institute of Technology - Stuart School of Business, IIT ( email )

10 West 35th Street, 18th Floor
Chicago, IL 60616
United States

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