Simulating and Analyzing Order Book Data: The Queue-Reactive Model

Abstract

Through the analysis of a dataset of ultra high frequency order book updates, we introduce a model which accommodates the empirical properties of the full order book together with the stylized facts of lower frequency financial data. To do so, we split the time interval of interest into periods in which a well chosen reference price, typically the midprice, remains constant. Within these periods, we view the limit order book as a Markov queuing system. Indeed, we assume that the intensities of the order flows only depend on the current state of the order book. We establish the limiting behavior of this model and estimate its parameters from market data. Then, in order to design a relevant model for the whole period of interest, we use a stochastic mechanism that allows to switch from one period of constant reference price to another. Beyond enabling to reproduce accurately the behavior of market data, we show that our framework can be very useful for practitioners, notably as a market simulator or as a tool for the transaction cost analysis of complex trading algorithms.

Modelling intensities of order flows in a limit order book

“…In this paper we propose a general model in line with previous contributions such as Mike & Farmer (2008), Huang et al (2015). We do not extend or specify previous models but build directly from the data.…”

“…The core of the submission mechanism in the order book remains however a Poisson process. Recently, Huang et al (2015) have proposed a model in which the intensities of submission of limit, market orders and cancellations depend on the volume of the first limit. They are able to show that a queueing system with these intensities is able to reproduce some empirical features of the limit order book, such as the distribution of the first level.…”

Reconstruction of Order Flows using Aggregated Data

“…Two examples of such works include limit order book modelling (see e.g. Cont et al (2010), Muni Toke (2015), Huang et al (2015) among many others) or order flow modelling with Hawkes processes (see references in Section 6).…”

A Reduced-Form Model for Level-1 Limit Order Books

“…With the empirical finding of approximate scale invariance, Bouchaud et al [7] derive a two dimensional Fokker-Planck equation describing the statistical behavior of the queue dynamic. In the recent work by Huang et al [10], they introduced a model which accommodates the empirical properties of the full order book and the stylized facts of lower frequency financial data. In their model, the order flows have statedependent intensities.…”