General Compound Hawkes Processes in Limit Order Books
Department of Mathematics and Statistics, Faculty of Science, Calgary, AL T2N1N4, Canada
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Author to whom correspondence should be addressed.
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These authors contributed equally to this work.
Risks 2020, 8(1), 28; https://doi.org/10.3390/risks8010028
Received: 29 January 2020 / Revised: 4 March 2020 / Accepted: 11 March 2020 / Published: 14 March 2020
(This article belongs to the Special Issue Stochastic Modelling in Financial Mathematics)
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 regard 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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Keywords:
Hawkes processes; general compound Hawkes processes; limit order books; functional central limit theorems; LOBSTER data
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MDPI and ACS Style
Swishchuk, A.; Huffman, A. General Compound Hawkes Processes in Limit Order Books. Risks 2020, 8, 28. https://doi.org/10.3390/risks8010028
AMA Style
Swishchuk A, Huffman A. General Compound Hawkes Processes in Limit Order Books. Risks. 2020; 8(1):28. https://doi.org/10.3390/risks8010028
Chicago/Turabian StyleSwishchuk, Anatoliy; Huffman, Aiden. 2020. "General Compound Hawkes Processes in Limit Order Books" Risks 8, no. 1: 28. https://doi.org/10.3390/risks8010028
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