A Stochastic Model for Order Book Dynamics

23 Pages Posted: 26 Sep 2008 Last revised: 31 Aug 2009

Rama Cont

Imperial College London; CNRS; Norges Bank Research

Sasha Stoikov

Cornell Financial Engineering Manhattan

Rishi Talreja

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Date Written: September 24, 2008

Abstract

We propose a stochastic model for the continuous-time dynamics of a limit order book. The model strikes a balance between three desirable features: it can be estimated easily from data, it captures key empirical properties of order book dynamics and its analytical tractability allows for fast computation of various quantities of interest without resorting to simulation. We describe a simple parameter estimation procedure based on high-frequency observations of the order book and illustrate the results on data from the Tokyo stock exchange. Using Laplace transform methods, we are able to efficiently compute probabilities of various events, conditional on the state of the order book: an increase in the mid-price, execution of an order at the bid before the ask quote moves, and execution of both a buy and a sell order at the best quotes before the price moves. Using high-frequency data, we show that our model can effectively capture the short-term dynamics of a limit order book. We also evaluate the performance of a simple trading strategy that is based on our results.

Keywords: High frequency data, limit order book, financial engineering, Laplace transform

JEL Classification: C44, C51, C32

Suggested Citation

Cont, Rama and Stoikov, Sasha and Talreja, Rishi, A Stochastic Model for Order Book Dynamics (September 24, 2008). Available at SSRN: https://ssrn.com/abstract=1273160 or http://dx.doi.org/10.2139/ssrn.1273160

Rama Cont (Contact Author)

Imperial College London ( email )

London, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/r.cont

CNRS ( email )

Laboratoire de Probabilites & Modeles aleatoires
Universite Pierre & Marie Curie (Paris VI)
Paris, 75252
France

HOME PAGE: http://rama.cont.perso.math.cnrs.fr/

Norges Bank Research ( email )

P.O. Box 1179
Oslo, N-0107
Norway

Sasha Stoikov

Cornell Financial Engineering Manhattan ( email )

55 Broad street (3rd floor)
New York, NY New York 10005
United States

Rishi Talreja

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

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