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Compound Hawkes Processes for Limit Order Book Flow and Volatility

Article arXiv papers · Author: Anatoliy Swishchuk et al.
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Summary

The paper develops general compound Hawkes processes and studies their properties in limit order books. It establishes a law of large numbers and functional central limit theorems for several specific versions of these processes, providing a mathematical framework for analyzing order arrivals and their aggregate behavior.

The authors apply the limit results to connect order flow with price volatility, expressing mid-price volatility through parameters for arrival rates and the mid-price process. The document gives theoretical results and describes their application, but the excerpt does not specify the model variants, assumptions, data, or empirical validation. It therefore supports conceptual understanding of the framework, while offering too little detail to assess how well it fits real markets or how it could be used in a trading strategy.

Key ideas

  • The paper constructs general compound Hawkes processes for modeling events in limit order books.
  • It proves law of large numbers and functional central limit results for selected process variants.
  • The framework is applied to relate order arrival behavior to mid-price volatility.
  • The volatility expression depends on arrival-rate and mid-price process parameters.

Tags

StatisticsMarket microstructureVolatilityHigh-frequency trading
Full text
# General Compound Hawkes Processes in Limit Order Books


# General Compound Hawkes Processes in Limit Order Books









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.

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