Compound Hawkes Processes in Limit Order Books

TL;DR

This paper introduces two new Hawkes process models for limit order book prices, deriving their theoretical properties and applying them to analyze the relationship between price volatility and order flow.

Contribution

It presents novel compound and regime-switching compound Hawkes processes, along with Law of Large Numbers and FCLT proofs, for modeling and analyzing limit order book prices.

Findings

Derived diffusion limits linking price volatility to order flow parameters

Established asymptotic theorems for the new Hawkes process models

Provided numerical examples illustrating the models' applications

Abstract

In this paper we introduce two new Hawkes processes, namely, compound and regime-switching compound Hawkes processes, to model the price processes in limit order books. We prove Law of Large Numbers and Functional Central Limit Theorems (FCLT) for both processes. The two FCLTs are applied to limit order books where we use these asymptotic methods to study the link between price volatility and order flow in our two models by using the diffusion limits of these price processes. The volatilities of price changes are expressed in terms of parameters describing the arrival rates and price changes. We also present some numerical examples.