Liquidity provision in a limit order book without adverse selection

Abstract

In this paper, we develop a dynamic model of a limit order market populated with liquidity traders who have only private values. We characterize and analyze the equilibrium order placement strategies of traders and the conditional execution probabilities of limit orders as a function of traders’ liquidity demand and the state of the limit order book. We solve for the equilibrium of the model numerically, and analyze its properties by performing comparative dynamics analysis. Our analysis shows that changes in the steady state of the limit order book and optimal order placement strategies reflect corresponding changes in the trade-off between order execution risk and the size of potential trading gains. The equilibrium order flow depends on the current state of the limit order book since a trader's optimal trading strategy is largely affected by the time and price priorities of the existing limit orders in the book. We demonstrate how changes in the dispersion of traders’ private values affect optimal trading strategies and conditional execution probabilities of limit orders. Our main result is that the dispersion in private values across traders has a significant impact on the stationary state of the equilibrium limit order book and the average bid–ask spread. A wider distribution of private values leads to more order placement at prices away from the consensus value, and therefore, to a larger bid–ask spread. Further, our numerical simulations show that extending the life span of limit orders reduces the average bid–ask spread observed in equilibrium. Finally, we find that the equilibrium percentage of market order submissions is also increasing in the dispersion in liquidity traders’ private values.