The Microstructure of Endogenous Liquidity Provision

Abstract

This paper generalizes the securities trading models with asymmetry information through relaxing the usual assumption of no-order-type-choice and allowing endogenous liquidity providers (ELPs) to switch between liquidity provision and consumption after observing private signals. We start with a simplified model with a discrete payoff structure, which generates a tractable non-linear equilibrium that explain the concave price function documented in the empirical literature. We further apply reinforcement learning technique, which does not rely on the typical “conjecture and verify” method, to generate the non-linear equilibrium with a continuously pay-off structure. The ex-post switching of the ELPs leads to endogenous uncertainty in different equilibrium regimes, significantly influences the adverse selection faced by designated market makers (DMMs), and generates a gap between liquidity provision from the DMMs and liquidity consumption by other traders. Therefore, the market breaks when ELPs switch from liquidity provision to liquidity consumption as a consequence of unexpected shocks.

Keywords: Endogenous liquidity provision, non-linear equilibrium, machine learning

JEL Classification: D82, D84, G10, G14