Multivariate General Compound Point Processes in Limit Order Books

Qi Guo, Bruno Remillard and Anatoliy Swishchuk
Additional contact information
Qi Guo: Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada
Bruno Remillard: Department of Decision Sciences, HEC Montréal, 3000 Chemin de la Cote-Sainte-Catherine, Montréal, QC H3T 2A7, Canada
Anatoliy Swishchuk: Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada

Risks, 2020, vol. 8, issue 3, 1-20

Abstract: 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.

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) (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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