Price Dynamics in a Markovian Limit Order Market
Imperial College London; CNRS
Adrien De Larrard
Université Paris VII Denis Diderot
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.
Number of Pages in PDF File: 23
Keywords: limit order book, market microstructure, queueing, diffusion limit, high-frequency data, liquidity, duration analysis, point process
JEL Classification: G1
Date posted: January 7, 2011 ; Last revised: March 28, 2012
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