A Dynamic Model of the Limit Order Book

Abstract

This paper presents a model of an order-driven market where fully strategic, symmetrically informed liquidity traders dynamically choose between limit and market orders, trading off execution price and waiting costs. In equilibrium the bid and ask prices depend only on the numbers of buy and sell orders in the book. The model has a number of empirical predictions: (i) higher trading activity and higher trading competition cause smaller spreads and lower price impact; (ii) market orders lead to a temporary price impact larger than the permanent price impact, therefore to price overshooting; (iii) buy and sell orders can cluster away from the bid-ask spread, generating a hump-shaped order book; (iv) bid and ask prices display a comovement effect: after e.g. a sell market order moves the bid price down, the ask price also falls, by a smaller amount, so the bid-ask spread widens; (v) when the order book is full, traders may submit quick, or fleeting, limit orders.

Keywords: Liquidity, waiting costs, price impact, order driven market, price overshooting, fleeting orders

JEL Classification: C7, D4, G1