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General Compound Hawkes Processes in Limit Order Books
Open AccessArticle

Multivariate General Compound Point Processes in Limit Order Books

1
Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada
2
Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Cote-Sainte-Catherine, Montréal, QC H3T 2A7, Canada
*
Author to whom correspondence should be addressed.
Risks 2020, 8(3), 98; https://doi.org/10.3390/risks8030098
Received: 29 July 2020 / Revised: 8 September 2020 / Accepted: 8 September 2020 / Published: 11 September 2020
(This article belongs to the Special Issue Stochastic Modelling in Financial Mathematics)
In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data. View Full-Text
Keywords: point process (PP); multivariate point processes (MPP); multivariate general compound point processes (MGCPP); limit order books (LOB); functional central limit theorems (FCLT); law of large numbers (LLN) point process (PP); multivariate point processes (MPP); multivariate general compound point processes (MGCPP); limit order books (LOB); functional central limit theorems (FCLT); law of large numbers (LLN)
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MDPI and ACS Style

Guo, Q.; Remillard, B.; Swishchuk, A. Multivariate General Compound Point Processes in Limit Order Books. Risks 2020, 8, 98. https://doi.org/10.3390/risks8030098

AMA Style

Guo Q, Remillard B, Swishchuk A. Multivariate General Compound Point Processes in Limit Order Books. Risks. 2020; 8(3):98. https://doi.org/10.3390/risks8030098

Chicago/Turabian Style

Guo, Qi; Remillard, Bruno; Swishchuk, Anatoliy. 2020. "Multivariate General Compound Point Processes in Limit Order Books" Risks 8, no. 3: 98. https://doi.org/10.3390/risks8030098

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