Long-Time Behavior of a Hawkes Process--Based Limit Order Book

Abstract

International audienceHawkes processes provide a natural framework to model dependenciesbetween the intensities of point processes. In the contextof order-driven financial markets, the relevance of such dependencieshas been amply demonstrated from an empirical, as well as theoretical,standpoint. In this work, we build on previous empirical and numericalstudies and introduce a mathematical model of limit order books basedon Hawkes processes with exponential kernels. After proving a generalstationarity result, we focus on the long-time behaviour of the limit orderbook and the corresponding dynamics of the suitably rescaled price.A formula for the asymptotic (in time) volatility of the price dynamicsinduced by that of the order book is obtained, involving the average offunctions of the various order book events under the stationary distribution

A Scaling Limit for Limit Order Books Driven by Hawkes Processes

“…For instance, φ Depending on the choice of that kernel, this allows us to model the arrival of "child market orders triggered by the arrival of a parent market order". 2 The factor |δ (n)…”

Order flow analysis of cryptocurrency markets

“…Theoretical study of limit order books is motivated by replicating the processes observed in a LOB by means of a mathematical process. Many scientists converge that processes within LOB can be modelled by characteristics of a Markov process (Huang et al 2015;Kelly and Yudovina 2017;Cont and De Larrard 2013), by those of a Hawkes process (Abergel and Jedidi 2015) and the hybrid of the two that evolves into a marked-point process (Morariu-Patrichi and Pakkanen 2017). Results are formulated by means of mathematical analysis.…”

High-dimensional Hawkes processes for limit order books: modelling, empirical analysis and numerical calibration

“…We refer the interested readers to Brémaud and Massoulié (1996), Massoulié (1998) for a more in-depth presentation of these processes, and to Zheng et al (2014), Abergel and Jedidi (2015) Bacry et al (2016) for recent applications to order book modelling.…”

“…To name a few, Bacry and Muzy (2014), Bacry et al (2013Bacry et al ( , 2016 propose various models of price and order flow models, whereas Bacry et al (2015) is an extensive survey of the application of Hawkes process in finance. In the specific context of limit order books, Large (2007) is an early study of Hawkes processes applied to order book modelling, Hawkes-process-based limit order book models are introduced and mathematically investigated in Abergel and Jedidi (2015), Zheng et al (2014) and, in a sligthly different direction, Rambaldi et al (2016) models the order volumes -in addition to their types -based on a multivariate Hawkes process.…”