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

Maxime Morariu-Patrichi () and Mikko Pakkanen ()
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Maxime Morariu-Patrichi: Imperial College London, Postal: Department of Mathematics, South Kensington Campus, London SW7 2AZ, United Kingdom
Mikko Pakkanen: Imperial College London and CREATES, Postal: Department of Mathematics, Office 801, Level 8, Weeks Building, South Kensington Campus, London SW7 2AZ, United Kingdom

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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. MSC 2010 Classification: 60G55, 62M09, 62P05

Keywords: Hawkes process; high-frequency financial data; market microstructure; limit order book; maximum likelihood estimation; endogeneity (search for similar items in EconPapers)
JEL-codes: C58 C51 G17 (search for similar items in EconPapers)
Date: 2018-09-21
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