A Level-1 Limit Order Book with Time Dependent Arrival Rates

Jonathan A. Chávez-Casillas, University of Rhode Island
Robert J. Elliott, Haskayne School of Business
Bruno Rémillard, HEC Montréal
Anatoliy V. Swishchuk, University of Calgary

Abstract

We propose a simple stochastic model for the dynamics of a limit order book, extending the recent work of Cont and de Larrard (SIAM J Financial Math 4(1), 1–25 2013), where the price dynamics are endogenous, resulting from market transactions. We also show that the conditional diffusion limit of the price process is the so-called Brownian meander.