Price Dynamics in a Markovian Limit Order Market

23 Pages Posted: 7 Jan 2011 Last revised: 28 Mar 2012

See all articles by Rama Cont

Rama Cont

University of Oxford

Adrien de Larrard

Université Paris VII Denis Diderot

Date Written: February 2012


We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical expressions for various quantities of interest such as the distribution of the duration between price changes, the distribution and autocorrelation of price changes, and the probability of an upward move in the price, conditional on the state of the order book. We study the diffusion limit of the price process and express the volatility of price changes in terms of parameters describing the arrival rates of buy and sell orders and cancelations. These analytical results provide some insight into the relation between order flow and price dynamics in order-driven markets.

Keywords: limit order book, market microstructure, queueing, diffusion limit, high-frequency data, liquidity, duration analysis, point process

JEL Classification: G1

Suggested Citation

Cont, Rama and de Larrard, Adrien, Price Dynamics in a Markovian Limit Order Market (February 2012). Available at SSRN: or

Rama Cont (Contact Author)

University of Oxford ( email )

Mathematical Institute
Oxford, OX2 6GG
United Kingdom

HOME PAGE: http://

Adrien De Larrard

Université Paris VII Denis Diderot ( email )

2, place Jussieu
Paris, 75005

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