Skip to content
All library documents

Compound Hawkes Processes for Limit Order Book Price Dynamics

Article arXiv papers · Author: Anatoliy Swishchuk et al.
Read the original

Summary

This paper introduces compound and regime-switching compound Hawkes processes as models for price dynamics in limit order books. Hawkes processes represent event arrivals whose rates can depend on prior events; the compound variants are used here to connect order flow with price changes. The paper establishes a law of large numbers and functional central limit theorems for both models.

The authors apply the limiting results to derive diffusion approximations for prices and examine how price volatility relates to order-flow arrival rates and price-change parameters. They also provide numerical examples. This offers a mathematical framework for studying how clustered order activity can shape price variation, with possible relevance to market microstructure and execution research. The supplied description does not report empirical validation on market data or details of the numerical results, so it does not establish how accurately the models describe a particular live order book.

Key ideas

  • The paper models limit order book prices using compound and regime-switching compound Hawkes processes.
  • It proves law of large numbers and functional central limit results for both process types.
  • Diffusion limits connect price volatility to order-flow arrival rates and price-change parameters.
  • Numerical examples illustrate the framework, but the description does not report validation against market data.

Tags

Market microstructureStatisticsVolatility
Full text
# Compound Hawkes Processes in Limit Order Books


# Compound Hawkes Processes in Limit Order Books









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.