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

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