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General Compound Hawkes Processes in Limit Order Books

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  • Anatoliy Swishchuk
  • Aiden Huffman

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.

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  • Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    • Handle: RePEc:arx:papers:1812.02298
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    References listed on IDEAS

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    Cited by:

    1. Anatoliy Swishchuk & Aiden Huffman, 2020. "General Compound Hawkes Processes in Limit Order Books," Risks, MDPI, vol. 8(1), pages 1-25, March.
    2. Anatoliy Swishchuk, 2020. "Stochastic Modelling of Big Data in Finance," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1613-1630, December.
    3. Qiyue He & Anatoliy Swishchuk, 2019. "Quantitative and Comparative Analyses of Limit Order Books with General Compound Hawkes Processes," Risks, MDPI, vol. 7(4), pages 1-21, November.
    4. Timothy DeLise, 2024. "The Negative Drift of a Limit Order Fill," Papers 2407.16527, arXiv.org.

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