I propose a continuous-time model of price formation in a market where trading is conducted according to a limit-order book. Strategic liquidity traders arrive randomly in the market and dynamically choose between limit and market orders, trading off execution price with waiting costs. I prove the existence of a Markov equilibrium in which the bid and ask prices depend only on the numbers of buy and sell orders in the book, and which can be characterized in closed-form in several cases of interest. The model generates empirically verified implications for the shape of the limit-order book and the dynamics of prices and trades. In particular, I show that buy and sell orders can cluster away from the bid-ask spread, thus generating a hump-shaped limit-order book. Also, consistent with Dufour and Engle (2000), if the time duration between trades decreases, the price impact of trades increases. Finally, following a market buy order, both the ask and bid prices increase, with the ask increasing more than the bid - hence the spread widens.
Published by ssrn.org
on 11/8/2005A Dynamic Model of the Limit Order Book