Limit Order Book as a Market for Liquidity

Abstract

We devel op a dynamic modelof anorder-drivenmarket populated bydiscretionary liquidity traders. These tradersmust trade, yet canchoose the type oforder and are fully strategic in their decision. Traders differ by their impatience: less patient traders are likely to demand liquidity, more patient traders are more likely to provide it. Three equilibrium patterns are obtained - the pattern is determined by three parameters: the degree of impatience of the patient traders, which we model as the cost of execution delay in providing liquidity; their proportion in the population, which determines the degree of competition among the liquidity providers; and the tick size, which is the cost of the minimal price improvement. Despite its simplicity, the model generates a rich set of empirical predictions on the relation between market parameters, time to execution, and spreads. We argue that the economic intuition of this model is robust, thus its main results will remain in more general models.

Keywords: Limit Orders, Market Orders, Liquidity, Order-Driven Markets, Tick Size, Impatience, Traders Arrival Rate, Price Improvement

JEL Classification: G10, G20