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

Igor Halperin

Chapter 2 in Reviews in Modern Quantitative Finance, 2024, pp 97-149 from World Scientific Publishing Co. Pte. Ltd.

Abstract: This chapter presents an analytically tractable and practically oriented model of nonlinear 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 nonlinear 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 nonlinearity 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 benign or distressed market environments, while using only a single volatility parameter.

Keywords: Quantitative Finance; Financial Engineering; Mathematical Finance; Computational Finance; Computational Methods; Computational Problems; Pricing of Securities; Trading; Market Microstructures; Risk Theory; Queuing Theory; Asset Management Technique; Liability Management Technique; Risk Measures; Solvency; Financial Instability; Fintech; Cryptocurrencies; Financial Machine Learning; Artificial Intelligence; Fintech; Quantum Computing; Distributed Ledgers; Econophysics (search for similar items in EconPapers)
JEL-codes: C C02 C6 C61 (search for similar items in EconPapers)
Date: 2024
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