Phases of Manes: Multi-Asset Non-Equilibrium Skew Model of a Strongly Non-Linear Market with Phase Transitions

38 Pages Posted: 18 Apr 2022

Multiple version iconThere are 2 versions of this paper

Abstract

This paper presents an analytically tractable and practically-oriented model of non-linear dynamics of a multi-asset market in the limit of a large number of assets. The asset price dynamics are driven by money flows into the market from external investors, and their price impact. This leads to a model of a market as an ensemble of interacting non-linear oscillators with the Langevin dynamics. In a homogeneous portfolio approximation, the mean field treatment of the resulting Langevin dynamics produces the McKean-Vlasov equation as a dynamic equation for market returns. Due to the strong non-linearity of the McKean-Vlasov equation, the resulting dynamics give rise to ergodicity breaking and first- or second-order phase transitions under variations of model parameters. Using a tractable potential of the Non-Equilibrium Skew (NES) model previously suggested by the author for a single-stock case, the new Multi-Asset NES (MANES) model enables an analytically tractable framework for a multi-asset market. The equilibrium expected market log-return is obtained as a self-consistent mean field of the McKean-Vlasov equation, and derived in closed form in terms of parameters that are inferred from market prices of S&P 500 index options. The model is able to accurately fit the market data for either a benign or distressed market environments, while using only a single volatility parameter.

Keywords: Non-equilibrium market dynamics, Langevin dynamics, mean field, Statistical Mechanics, McKean-Vlasov equation

Suggested Citation

Halperin, Igor, Phases of Manes: Multi-Asset Non-Equilibrium Skew Model of a Strongly Non-Linear Market with Phase Transitions. Available at SSRN: https://ssrn.com/abstract=4086597 or http://dx.doi.org/10.2139/ssrn.4086597

Igor Halperin (Contact Author)

Fidelity Investments, Inc. ( email )

United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
446
Abstract Views
1,092
Rank
44,177
PlumX Metrics