  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.
