“Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons

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 incorporates 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.

Financial Markets and the Phase Transition between Water and Steam

“…Other models, in which the deviation of the asset price from its long-term mean moves in a polynomial potential have previously been considered [27,28,29,30]. There, various potentials were found for shorter time windows, whose coefficients depend on the asset and the time window.…”

Modeling Asymmetric Interactions in Economy

“…Reference [12] modeled a financial market. It was treated as an open system with money exchange with the outside, and a non-equilibrium model was applied.…”

Non-Equilibrium Skewness, Market Crises, and Option Pricing: Non-Linear Langevin Model of Markets with Supersymmetry

“…Note that while a Langevin model with a non-linear potential could be introduced based on phenomenological grounds, the approach of this paper is motivated by previous work in [16] and [17] that developed a non-linear Langevin model of stock price dynamics. A model developed in [16,17], called the QED ("Quantum Equilibrium-Disequilibrium") model, explains non-linearities of price dynamics as a combined effect of capital inflows or outflows in the market, and their impact on asset returns, modeled as a linear or quadratic function of capital inflows. In [18], the single-stock QED model is generalized to an interacting multi-asset universe composed of 𝑁 risky assets, and re-formulated in terms of returns rather than prices.…”