Title: Market Microstructure Invariance: A Dynamic Equilibrium Model
Abstract: Invariance relationships are derived in a dynamic, infinite-horizon, equilibrium model of adverse selection with risk-neutral informed traders, noise traders, risk-neutral market makers, and endogenous information production. Scaling laws for bet size and transaction costs require the assumption that the effort required to generate one bet does not vary across securities and time. Scaling laws for pricing accuracy and market resiliency require the additional assumption that private information has the same signal-to-noise ratio across markets. Prices follow a martingale with endogenously derived stochastic volatility. Returns volatility, pricing accuracy, market depth, and market resiliency are closely related to one another. The model solution depends on two state variables: stock price and hard-to- observe pricing accuracy. Invariance makes predictions operational by expressing them in terms of log-linear functions of easily observable variables such as price, volume, and volatility.