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Related papers: Compound Hawkes Processes in Limit Order Books

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We introduce a multivariate Hawkes process that accounts for the dynamics of market prices through the impact of market order arrivals at microstructural level. Our model is a point process mainly characterized by 4 kernels associated with…

Trading and Market Microstructure · Quantitative Finance 2013-01-08 E. Bacry , J. F Muzy

In this paper, we introduce a new model for the risk process based on general compound Hawkes process (GCHP) for the arrival of claims. We call it risk model based on general compound Hawkes process (RMGCHP). The Law of Large Numbers (LLN)…

Risk Management · Quantitative Finance 2017-06-29 Anatoliy Swishchuk

Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to…

Trading and Market Microstructure · Quantitative Finance 2016-04-18 Roger Martins , Dieter Hendricks

We give functional laws of large numbers for a class of marked Hawkes processes and marked compound Hawkes processes with a general mark space. Our results provide some complement to those presented previously in the literature. As an…

Probability · Mathematics 2025-10-29 Tomasz R. Bielecki , Jacek Jakubowski , Mariusz iewȩgłowski , Anatoliy Swishchuk

We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$. We further exhibit the asymptotic behaviour of the…

Probability · Mathematics 2012-02-07 Emmanuel Bacry , Sylvain Delattre , Marc Hoffmann , Jean François Muzy

Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of…

Trading and Market Microstructure · Quantitative Finance 2015-10-14 Xin Guo , Zhao Ruan , Lingjiong Zhu

Hawkes processes are a class of point processes that have the ability to model the self- and mutual-exciting phenomena. Although the classic Hawkes processes cover a wide range of applications, their expressive ability is limited due to…

Machine Learning · Computer Science 2021-06-10 Feng Zhou , Quyu Kong , Yixuan Zhang , Cheng Feng , Jun Zhu

This paper develops a theoretical mesoscopic model of the limit order book driven by multivariate Hawkes processes, designed to capture temporal self-excitation and the spatial propagation of order flow across price levels. In contrast to…

Mathematical Finance · Quantitative Finance 2025-11-25 Levon Mahseredjian

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

This paper proposes an Extended State-Dependent Hawkes Process (ExsdHawkes) to model the intricate dynamics of Limit Order Books (LOBs). Our theoretical contribution lies in relaxing traditional constraints by allowing for state…

Applications · Statistics 2026-04-28 Akitoshi Kimura

This paper focuses on limit theorems for linear Hawkes processes with random marks. We prove a large deviation principle, which answers the question raised by Bordenave and Torrisi. A central limit theorem is also obtained. We conclude with…

Probability · Mathematics 2015-09-15 Dmytro Karabash , Lingjiong Zhu

The propagation of chaos and associated law of large numbers for mean-field interacting age-dependent Hawkes processes (when the number of processes n goes to +$\infty$) being granted by the study performed in (Chevallier, 2015), the aim of…

Probability · Mathematics 2016-11-08 Julien Chevallier

We present a reproducible research framework for market microstructure combining a deterministic C++ limit order book (LOB) simulator with stochastic order flow generated by multivariate marked Hawkes processes. The paper derives full…

Trading and Market Microstructure · Quantitative Finance 2025-10-10 Sohaib El Karmi

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

The Hawkes process is a self-exciting sample point process. It has wide applications in finance, social networks, criminology, seismology, and many other fields. With the development of storage technology, data-driven models are attracting…

Probability · Mathematics 2021-06-23 Haixu Wang

The order flow in high-frequency financial markets has been of particular research interest in recent years, as it provides insights into trading and order execution strategies and leads to better understanding of the supply-demand…

Methodology · Statistics 2025-02-26 Alex Ziyu Jiang , Abel Rodriguez

The Hawkes model is suitable for describing self and mutually exciting random events. In addition, the exponential decay in the Hawkes process allows us to calculate the moment properties in the model. However, due to the complexity of the…

Statistical Finance · Quantitative Finance 2024-09-24 Kyungsub Lee

Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…

Probability · Mathematics 2018-11-05 Fuqing Gao , Lingjiong Zhu

We derive a continuous time model for the joint evolution of the mid price and the bid-ask spread from a multiscale analysis of the whole limit order book (LOB) dynamics. We model the LOB as a multiclass queueing system and perform our…

Trading and Market Microstructure · Quantitative Finance 2013-10-07 Jose Blanchet , Xinyun Chen

In a discrete-time setting, we consider an arrival process $\left\{\xi_n \, \middle| \, n = 1, 2, \ldots \right\}$, which models the occurrence of events, and a corresponding point process $\left\{H_n \, \middle| \, n = 1, 2, \ldots…

Probability · Mathematics 2026-03-10 Utpal Jyoti Deba Sarma , Dharmaraja Selvamuthu