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State-dependent Hawkes processes and their application to limit order book modelling

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State-dependent Hawkes processes and their application to limit order book modelling. / Morariu-Patrichi, Maxime; Pakkanen, Mikko S.

In: Quantitative Finance, Vol. 22, No. 3, 2022, p. 563-583.

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Morariu-Patrichi M, Pakkanen MS. State-dependent Hawkes processes and their application to limit order book modelling. Quantitative Finance. 2022;22(3):563-583. doi: 10.1080/14697688.2021.1983199

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Morariu-Patrichi, Maxime ; Pakkanen, Mikko S. / State-dependent Hawkes processes and their application to limit order book modelling. In: Quantitative Finance. 2022 ; Vol. 22, No. 3. pp. 563-583.

Bibtex

@article{c4273b39d71e4c77b266ad2536ba4ef7,
title = "State-dependent Hawkes processes and their application to limit order book modelling",
abstract = "We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The excitation kernel of the counting process depends on the state process that, reciprocally, switches state when there is an event in the counting process. We first establish the existence and uniqueness of state-dependent Hawkes processes and explain how they can be simulated. Then we develop maximum likelihood estimation methodology for parametric specifications of the process. We apply state-dependent Hawkes processes to high-frequency limit order book data, allowing us to build a novel model that captures the feedback loop between the order flow and the shape of the limit order book. We estimate two specifications of the model, using the bid–ask spread and the queue imbalance as state variables, and find that excitation effects in the order flow are strongly state-dependent. Additionally, we find that the endogeneity of the order flow, measured by the magnitude of excitation, is also state-dependent, being more pronounced in disequilibrium states of the limit order book.",
keywords = "Endogeneity, Hawkes process, High-frequency financial data, Limit order book, Market microstructure, Maximum likelihood estimation",
author = "Maxime Morariu-Patrichi and Pakkanen, {Mikko S.}",
year = "2022",
doi = "10.1080/14697688.2021.1983199",
language = "English",
volume = "22",
pages = "563--583",
journal = "Quantitative Finance",
issn = "1469-7688",
publisher = "Routledge",
number = "3",

}

RIS

TY - JOUR

T1 - State-dependent Hawkes processes and their application to limit order book modelling

AU - Morariu-Patrichi, Maxime

AU - Pakkanen, Mikko S.

PY - 2022

Y1 - 2022

N2 - We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The excitation kernel of the counting process depends on the state process that, reciprocally, switches state when there is an event in the counting process. We first establish the existence and uniqueness of state-dependent Hawkes processes and explain how they can be simulated. Then we develop maximum likelihood estimation methodology for parametric specifications of the process. We apply state-dependent Hawkes processes to high-frequency limit order book data, allowing us to build a novel model that captures the feedback loop between the order flow and the shape of the limit order book. We estimate two specifications of the model, using the bid–ask spread and the queue imbalance as state variables, and find that excitation effects in the order flow are strongly state-dependent. Additionally, we find that the endogeneity of the order flow, measured by the magnitude of excitation, is also state-dependent, being more pronounced in disequilibrium states of the limit order book.

AB - We study statistical aspects of state-dependent Hawkes processes, which are an extension of Hawkes processes where a self- and cross-exciting counting process and a state process are fully coupled, interacting with each other. The excitation kernel of the counting process depends on the state process that, reciprocally, switches state when there is an event in the counting process. We first establish the existence and uniqueness of state-dependent Hawkes processes and explain how they can be simulated. Then we develop maximum likelihood estimation methodology for parametric specifications of the process. We apply state-dependent Hawkes processes to high-frequency limit order book data, allowing us to build a novel model that captures the feedback loop between the order flow and the shape of the limit order book. We estimate two specifications of the model, using the bid–ask spread and the queue imbalance as state variables, and find that excitation effects in the order flow are strongly state-dependent. Additionally, we find that the endogeneity of the order flow, measured by the magnitude of excitation, is also state-dependent, being more pronounced in disequilibrium states of the limit order book.

KW - Endogeneity

KW - Hawkes process

KW - High-frequency financial data

KW - Limit order book

KW - Market microstructure

KW - Maximum likelihood estimation

UR - http://www.scopus.com/inward/record.url?scp=85121339633&partnerID=8YFLogxK

U2 - 10.1080/14697688.2021.1983199

DO - 10.1080/14697688.2021.1983199

M3 - Journal article

AN - SCOPUS:85121339633

VL - 22

SP - 563

EP - 583

JO - Quantitative Finance

JF - Quantitative Finance

SN - 1469-7688

IS - 3

ER -