Order Book Dynamics in Liquid Markets: Limit Theorems and Diffusion Approximations

By Rama Cont, Adrien de Larrard. 2012

92 citations recorded by the source corpus.

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 underlying order flow. 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.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/8460962f47625927577d17fead613428947bb65c

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Citations in the corpus

A one-level limit order book model with memory and variable spread (2017, background): “We refer to Gould et al. [9] for a nice survey of the extensive literature on the subject, which, among the most relevant to our work, includes Luckock [13], Kruk [12], Smith et al. [19], Rosu [17], Cont et al. [7], Abergel and Jedidi [1], Cont and Larrard [6], and Cont and Larrard [5].”
Price Dynamics in a Markovian Limit Order Market (2011, background): “The state of the order book is modified by order book events: limit orders (at the bid or ask), market orders and cancelations (see Cont et al. (2010b,a), Smith et al. (2003)).”
Statistical inference for ergodic point processes and application to Limit Order Book (2015, background): “The seminal work about this basic representation [20] has been followed by many extensions, see for example [1, 6, 8, 7, 15].”
Data-Driven Market-Making via Model-Free Learning (2020, methodology): “However, in our particular application setting, no correlation for both the observations and their common variants (e.g., square, inverse) should sufﬁce as an indication of independence, in the same spirit of [ Cont and De Larrard, 2012 ] .”