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

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  • Igor Halperin

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.

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  • Igor Halperin, 2022. "Phases of MANES: Multi-Asset Non-Equilibrium Skew Model of a Strongly Non-Linear Market with Phase Transitions," Papers 2203.07550, arXiv.org.
    • Handle: RePEc:arx:papers:2203.07550
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    References listed on IDEAS

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    1. Frazzini, Andrea & Lamont, Owen A., 2008. "Dumb money: Mutual fund flows and the cross-section of stock returns," Journal of Financial Economics, Elsevier, vol. 88(2), pages 299-322, May.
    2. Halperin, Igor, 2022. "Non-equilibrium skewness, market crises, and option pricing: Non-linear Langevin model of markets with supersymmetry," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 594(C).
    3. Halperin, Igor & Dixon, Matthew, 2020. "“Quantum Equilibrium-Disequilibrium”: Asset price dynamics, symmetry breaking, and defaults as dissipative instantons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
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