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In this paper we propose a dynamic model of Limit Order Book (LOB). The main feature of our model is that the shape of the LOB is determined endogenously by an expected utility function via a competitive equilibrium argument. Assuming zero…

Optimization and Control · Mathematics 2014-01-23 Jin Ma , Xinyang Wang , Jianfeng Zhang

Financial market simulation (FMS) serves as a promising tool for understanding market anomalies and the underlying trading behaviors. To ensure high-fidelity simulations, it is crucial to calibrate the FMS model for generating data closely…

Computational Engineering, Finance, and Science · Computer Science 2025-06-17 Yuanzhe Li , Yue Wu , Muyao Zhong , Shengcai Liu , Peng Yang

We propose a framework for studying optimal market making policies in a limit order book (LOB). The bid-ask spread of the LOB is modelled by a Markov chain with finite values, multiple of the tick size, and subordinated by the Poisson…

Trading and Market Microstructure · Quantitative Finance 2011-06-29 Fabien Guilbaud , Huyen Pham

The extent to which a matching engine can cloud the modelling of underlying order submission and management processes in a financial market remains an unanswered concern with regards to market models. Here we consider a 10-variate Hawkes…

Trading and Market Microstructure · Quantitative Finance 2021-08-18 Ivan Jericevich , Patrick Chang , Tim Gebbie

The limit order book (LOB) depicts the fine-grained demand and supply relationship for financial assets and is widely used in market microstructure studies. Nevertheless, the availability and high cost of LOB data restrict its wider…

Trading and Market Microstructure · Quantitative Finance 2021-07-02 Zijian Shi , John Cartlidge

A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process…

Trading and Market Microstructure · Quantitative Finance 2026-05-12 Luca Mucciante , Alessio Sancetta

Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that…

Statistical Finance · Quantitative Finance 2015-03-13 Thibault Jaisson , Mathieu Rosenbaum

In this paper we derive a scaling limit for an infinite dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume…

Mathematical Finance · Quantitative Finance 2018-08-09 Ulrich Horst , Wei Xu

This paper studies the fill probabilities of limit orders placed at different price levels in a limit order book. These probabilities play a central role in execution optimization, as limit orders are not guaranteed to be executed and…

Trading and Market Microstructure · Quantitative Finance 2026-02-09 Felix Lokin , Fenghui Yu

In the rapidly evolving world of financial markets, understanding the dynamics of limit order book (LOB) is crucial for unraveling market microstructure and participant behavior. We introduce ClusterLOB as a method to cluster individual…

Trading and Market Microstructure · Quantitative Finance 2025-05-13 Yichi Zhang , Mihai Cucuringu , Alexander Y. Shestopaloff , Stefan Zohren

We introduce a Hawkes-like process and study its scaling limit as the system becomes increasingly endogenous. We derive functional limit theorems for intensity and fluctuations. Then, we introduce a high-frequency model for a price of a…

Probability · Mathematics 2018-07-12 Łukasz Treszczotko

Empirical data reveals that the liquidity flow into the order book (depositions, cancellations andmarket orders) is influenced by past price changes. In particular, we show that liquidity tends todecrease with the amplitude of past…

Trading and Market Microstructure · Quantitative Finance 2020-06-24 Antoine Fosset , Jean-Philippe Bouchaud , Michael Benzaquen

Limit order book (LOB) is a dynamic, event-driven system that records real-time market demand and supply for a financial asset in a stream flow. Event stream prediction in LOB refers to forecasting both the timing and the type of events.…

Statistical Finance · Quantitative Finance 2024-12-16 Zetao Zheng , Guoan Li , Deqiang Ouyang , Decui Liang , Jie Shao

The Tick library allows researchers in market microstructure to simulate and learn Hawkes process in high-frequency data, with optimized parametric and non-parametric learners. But one challenge is to take into account the correct causality…

Machine Learning · Statistics 2021-01-19 Marcos Costa Santos Carreira

This paper investigates real-time detection of spoofing activity in limit order books, focusing on cryptocurrency centralized exchanges. We first introduce novel order flow variables based on multi-scale Hawkes processes that account both…

Trading and Market Microstructure · Quantitative Finance 2025-04-23 Timothée Fabre , Damien Challet

We investigate the behavior of limit order books on the meso-scale motivated by order execution scheduling algorithms. To do so we carry out empirical analysis of the order flows from market and limit order submissions, aggregated from…

Trading and Market Microstructure · Quantitative Finance 2017-08-10 Kyle Bechler , Michael Ludkovski

This paper presents a novel model for simulating and analyzing sparse limit order books (LOBs), with a specific application to the European intraday electricity market. In illiquid markets, characterized by significant gaps between order…

Trading and Market Microstructure · Quantitative Finance 2024-10-10 Philippe Bergault , Enzo Cognéville

We show that multivariate Hawkes processes coupled with the nonparametric estimation procedure first proposed in Bacry and Muzy (2015) can be successfully used to study complex interactions between the time of arrival of orders and their…

Trading and Market Microstructure · Quantitative Finance 2018-07-10 Marcello Rambaldi , Emmanuel Bacry , Fabrizio Lillo

This article presents a Hawkes process model with Markovian baseline intensities for high-frequency order book data modeling. We classify intraday order book trading events into a range of categories based on their order types and the price…

Trading and Market Microstructure · Quantitative Finance 2022-01-07 Philip Protter , Qianfan Wu , Shihao Yang

In this work we introduce two variants of multivariate Hawkes models with an explicit dependency on various queue sizes aimed at modeling the stochastic time evolution of a limit order book. The models we propose thus integrate the…

Trading and Market Microstructure · Quantitative Finance 2019-01-28 Peng Wu , Marcello Rambaldi , Jean-François Muzy , Emmanuel Bacry