Order book dynamics in liquid markets: limit theorems and diffusion approximations

Abstract : We propose a model for the dynamics of a limit order book in a liquid market where buy and sell orders are submitted at high frequency. We derive a functional central limit theorem for the joint dynamics of the bid and ask queues and show that, when the frequency of order arrivals is large, the intraday dynamics of the limit order book may be approximated by a Markovian jump-diffusion process in the positive orthant, whose characteristics are explicitly described in terms of the statistical properties of the order flow and only depend on rate of arrival of orders and the covariance structure of order sizes. This result allows to obtain tractable analytical approximations for various quantities of interest, such as the probability of a price increase or the distribution of the duration until the next price move, conditional on the state of the order book. Our results allow for a wide range of distributional assumptions and temporal dependence in the order flow and apply to a wide class of stochastic models proposed for order book dynamics, including models based on Poisson point processes, self-exciting point processes and models of the ACD-GARCH family.
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00672274
Contributeur : Rama Cont <>
Soumis le : lundi 1 octobre 2012 - 21:48:09
Dernière modification le : jeudi 27 avril 2017 - 09:45:51
Document(s) archivé(s) le : vendredi 16 décembre 2016 - 19:25:42

Fichier

HeavyTrafficOrderBook.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00672274, version 2

Collections

UPMC | INSMI | LARA | USPC | PMA

Citation

Rama Cont, Adrien De Larrard. Order book dynamics in liquid markets: limit theorems and diffusion approximations. 2011. <hal-00672274v2>

Partager

Métriques

Consultations de
la notice

261

Téléchargements du document

193