“Market Making” in an Order Book Model and Its Impact on the Spread

Abstract

It has been suggested that marked point processes might be good candidates for the modelling of financial high-frequency data. A special class of point processes, Hawkes processes, has been the subject of various investigations in the financial community. In this paper, we propose to enhance a basic zero-intelligence order book simulator with arrival times of limit and market orders following mutually (asymmetrically) exciting Hawkes processes. Modelling is based on empirical observations on time intervals between orders that we verify on several markets (equity, bond futures, index futures). We show that this simple feature enables a much more realistic treatment of the bid-ask spread of the simulated order book.

Quantification of the High Level of Endogeneity and of Structural Regime Shifts in Commodity Markets

“…Nowadays, the Hawkes point process has become the "gold standard" of selfexcited models to describe discontinuous financial data. It has a wide range of applications going from modeling high frequency order flows (Hewlett, 2006;Bauwens and Hautsch, 2009) and the construction process of the order book (Large, 2007;Toke, 2011;Cont, 2011), to modeling extreme events clustering at daily and hourly scales (Embrechts et al, 2011), estimating Value-at-Risk (Chavez-Demoulin et al, 2005) or modeling correlated default times in a portfolio of firms (Errais et al, 2010;Azizpour et al, 2011).…”

Statistical inference for ergodic point processes and application to Limit Order Book

“…Despite their mathematical tractability, such models are too simple to be entirely satisfactory, essentially because of the absence of any structure of dependence in the order submission process. Lately more complex dynamics have been proposed, including Markovian models [16], Hawkes process driven bid-ask prices [5,40], or even Hawkes processes-based LOB models [2,35,6], the latter being reputed to efficiently capture the time clustering property of orders, and the cross-dependences in the order flow.…”

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

“…The main reason is that they allow one to account for the mutual influence of various types of events in a simple and parsimonious way through a conditional intensity vector. Hawkes processes have been involved in many different problems of high frequency finance ranging from the simple description of the temporal occurrence of market orders or price changes (Bowsher (2007), Hardiman and Bouchaud (2014), Filimonov and Sornette (2012)), to the complex modelling of the arrival rates of various kinds of events in a full order book model (Large (2007), Toke (2011), Jedidi and Abergel (2013)). We refer to Bacry et al (2015b) for a recent review.…”