Reduced form modeling of limit order markets

This paper proposes a parametric approach for stochastic modeling of limit order markets. The models are obtained by augmenting classical perfectly liquid market models with a few additional risk factors that describe liquidity properties of the order book. The resulting models are easy to calibrate and to analyse using standard techniques for multivariate stochastic processes. Despite their simplicity, the models are able to capture several properties that have been found in microstructural analysis of limit order markets. Calibration of a continuous-time three-factor model to Copenhagen Stock Exchange data exhibits, for example, mean reversion in liquidity as well as the so-called crowding out effect, which influences subsequent mid-price moves. Our dynamic models are also well suited for analysing market resilience after liquidity shocks.

[1]  Joel Hasbrouck,et al.  Measuring the Information Content of Stock Trades , 1991 .

[2]  Charles M. C. Lee,et al.  Inferring Trade Direction from Intraday Data , 1991 .

[3]  R. Uppal,et al.  Optimal Replication of Options with Transactions Costs and Trading Restrictions , 1993, Journal of Financial and Quantitative Analysis.

[4]  L. Glosten.  Is the Electronic Open Limit Order Book Inevitable , 1994 .

[5]  Chester Spatt,et al.  An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse , 1995 .

[6]  E. Jouini,et al.  Martingales and Arbitrage in Securities Markets with Transaction Costs , 1995 .

[7]  D. Bertsimas,et al.  Optimal control of execution costs , 1998 .

[8]  Christine A. Parlour.  Price Dynamics in Limit Order Markets , 1998 .

[9]  Yuri Kabanov,et al.  Hedging and liquidation under transaction costs in currency markets , 1999, Finance Stochastics.

[10]  Gur Huberman,et al.  Optimal Liquidity Trading , 2000 .

[11]  Brian F. Smith,et al.  The costs and determinants of order aggressiveness , 2000 .

[12]  Thierry Foucault,et al.  Limit Order Book as a Market for Liquidity , 2001 .

[13]  Ohad Kadan,et al.  Limit Order Book as a Market for Liquidity , 2001 .

[14]  Patrik Sand̊as,et al.  Adverse Selection and Competitive Market Making: Empirical Evidence from a Limit Order Market , 2001 .

[15]  L. Gillemot,et al.  Statistical theory of the continuous double auction , 2002, cond-mat/0210475.

[16]  H. Luckock.  A steady-state model of the continuous double auction , 2003 .

[17]  Philip Protter,et al.  Noname manuscript No. (will be inserted by the editor) Liquidity Risk and Arbitrage Pricing Theory , 2003 .

[18]  Angelo Ranaldo,et al.  Order aggressiveness in limit order book markets , 2004 .

[19]  Jean-Philippe Bouchaud,et al.  Random walks, liquidity molasses and critical response in financial markets , 2004, cond-mat/0406224.

[20]  L. Glosten,et al.  Market Microstructure: A Survey of Microfoundations, Empirical Results, and Policy Implications , 2005 .

[21]  Lawrence Harris,et al.  The information content of the limit order book: evidence from NYSE specialist trading decisions ☆ , 2005 .

[22]  Alexander Fadeev,et al.  Optimal execution for portfolio transactions , 2006 .

[23]  Walter Schachermayer,et al.  The Mathematics of Arbitrage , 2006 .

[24]  P. Protter,et al.  Pricing Options in an Extended Black Scholes Economy with Illiquidity: Theory and Empirical Evidence , 2006 .

[25]  Alexander Schied,et al.  Optimal execution strategies in limit order books with general shape functions , 2007, 0708.1756.

[26]  L. Rogers,et al.  MODELING LIQUIDITY EFFECTS IN DISCRETE TIME , 2007 .

[27]  Ryan Gill,et al.  Computation of estimates in segmented regression and a liquidity effect model , 2007, Comput. Stat. Data Anal..

[28]  Teemu Pennanen,et al.  SUPERHEDGING IN ILLIQUID MARKETS , 2008, 0807.2962.

[29]  A. Kempf,et al.  Liquidity Commonality Beyond Best Prices , 2008 .

[30]  J. Bouchaud,et al.  How Markets Slowly Digest Changes in Supply and Demand , 2008, 0809.0822.

[31]  Ioanid Roşu.  A Dynamic Model of the Limit Order Book , 2008 .

[32]  Philip Protter,et al.  AN ANALYSIS OF THE SUPPLY CURVE FOR LIQUIDITY RISK THROUGH BOOK DATA , 2010 .

[33]  Rama Cont,et al.  A Stochastic Model for Order Book Dynamics , 2008, Oper. Res..

[34]  Teemu Pennanen,et al.  Galerkin methods in dynamic stochastic programming , 2010 .

[35]  Y. Kabanov,et al.  Markets with transaction costs , 2010 .

[36]  Robert F. Engle,et al.  Analysis of High-Frequency Data , 2010 .

[37]  Teemu Pennanen,et al.  Arbitrage and deflators in illiquid markets , 2008, Finance Stochastics.