Multivariate General Compound Point Processes in Limit Order Books

TL;DR

This paper introduces the multivariate general compound point process (MGCPP) as a new model for order flow in limit order books, providing theoretical results and empirical comparisons with existing models using major tech stocks.

Contribution

It proposes MGCPP as an alternative to Hawkes processes for modeling order flow, with proven LLN and FCLTs, and demonstrates its application to real trading data.

Findings

MGCPP effectively models order flow in limit order markets.

Theoretical LLN and FCLTs are established for MGCPP.

Numerical simulations show MGCPP's competitive performance.

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. 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.