The role of volume in order book dynamics: a multivariate Hawkes process analysis

Abstract

We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in can be successfully used to study complex interactions between the time of arrival of orders and their size, observed in a limit order book market. We apply this methodology to high-frequency order book data of futures traded at EUREX. Specifically, we demonstrate how this approach is amenable not only to analyze interplay between different order types (market orders, limit orders, cancellations) but also to include other relevant quantities, such as the order size, into the analysis, showing also that simple models assuming the independence between volume and time are not suitable to describe the data.

Analysis of order book flows using a non-parametric estimation of the branching ratio matrix

“…This suggests that most inhibition effects are short lived and the effect of an event arrival is towards an increase of the overall intensity. This is in line with what was found in and Rambaldi et al (2016), where the inhibitions effects were shown to be mostly concentrated around the typical market reaction time.…”

“…For all events T a , L a and C a the most visible feature is the strong self-exciting interaction. This has been confirmed in several works , Rambaldi et al (2016)) and can be traced to order-splitting strategies and herding behaviors. Signatures of typical trading patterns can be seen also in the kernels L a → C a , L a → C b , where the positive value of the kernel arises form agents canceling and replacing their limit orders with or without switching sides.…”

“…These events occur in a very correlated manner (with long-range correlations) and the system dimensionality can vary from low to moderately high. In a series of recent papers, Bacry et al have shown that the non parametric Wiener-Hopf method provides reliable estimations in order to describe, within a multivariate Hawkes model, various aspects of level-I order book fluctuations: the coupled dynamics of mid-price changes, market and limit order arrivals (Bacry and Muzy (2014), ), the impact of market orders (Bacry et al (2015a)) or the interplay between book orders of different sizes (Rambaldi et al (2016)). However, if one wants to account for systems of larger dimensionality by considering for instance a wider class of event types or the book events associated with a basket (e.g.…”

Order-Book Modeling and Market Making Strategies

“…In the work of [Huang et al, 2015], and many other related works, the order size is supposed to be constant. It is however clear from empirical analyses that the order sizes have remarkable statistical properties, and that such information is relevant to the LOB dynamics, see for instance [Abergel et al, 2016][Muni Toke, 2015 [Rambaldi et al, 2017].…”

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

“…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.…”