# General Compound Hawkes Processes in Limit Order Books

## TL;DR

This paper introduces and analyzes general compound Hawkes processes within limit order books, establishing their theoretical properties and applying them to understand the relationship between price volatility and order flow.

## Contribution

It constructs new compound Hawkes processes, proves LLN and FCLT for these models, and links these results to price volatility analysis in limit order books.

## Key findings

- Established LLN and FCLT for compound Hawkes processes
- Linked price volatility to order flow parameters
- Provided theoretical foundation for modeling limit order books

## Abstract

In this paper, we study various new Hawkes processes. Specifically, we construct general compound Hawkes processes and investigate their properties in limit order books. With regards to these general compound Hawkes processes, we prove a Law of Large Numbers (LLN) and a Functional Central Limit Theorems (FCLT) for several specific variations. We apply several of these FCLTs to limit order books to study the link between price volatility and order flow, where the volatility in mid-price changes is expressed in terms of parameters describing the arrival rates and mid-price process.