Equilibrium in a Dynamic Limit Order Market

Abstract

We model a dynamic limit order market as a stochastic sequential game. Since the model is analytically intractable, we provide an algorithm based on Pakes and McGuire (2001) to find a stationary Markov-perfect equilibrium. Given the stationary equilibrium, we generate artificial time series and perform comparative dynamics. We demonstrate that the order flow displays persistence. As we know the data generating process, we can compare transaction prices to the true value of the asset, as well as explicitly determine the welfare gains accruing to investors. Due to the endogeneity of order flow, the midpoint of the quoted prices is not a good proxy for the true value. Further, transaction costs paid by market order submitters are negative on average. The effective spread is negatively correlated with true transaction costs, and largely uncorrelated with changes in investor surplus. As a policy experiment, we consider the effect of a change in tick size, and find that it has a very small positive impact on investor surplus.

Keywords: Limit order markets, computational

JEL Classification: G2, C6