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General Compound Hawkes Processes in Limit Order Books

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  • Anatoliy Swishchuk

Abstract

In this paper, we study various new Hawkes processes, namely, so-called general compound and regime-switching general compound Hawkes processes to model the price processes in the limit order books. We prove Law of Large Numbers (LLN) and Functional Central Limit Theorems (FCLT) for these processes. The latter 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 studying 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.

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  • Anatoliy Swishchuk, 2017. "General Compound Hawkes Processes in Limit Order Books," Papers 1706.07459, arXiv.org, revised Jun 2017.
    • Handle: RePEc:arx:papers:1706.07459
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    1. Engle, Robert F. & Lange, Joe, 2001. "Predicting VNET: A model of the dynamics of market depth," Journal of Financial Markets, Elsevier, vol. 4(2), pages 113-142, April.
    2. Vladimir Filimonov & Didier Sornette, 2012. "Quantifying reflexivity in financial markets: towards a prediction of flash crashes," Papers 1201.3572, arXiv.org, revised Apr 2012.
    3. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    4. Ban Zheng & Franc{c}ois Roueff & Fr'ed'eric Abergel, 2013. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Papers 1301.5007, arXiv.org, revised Feb 2014.
    5. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    6. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    7. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    8. Patrick J. Laub & Thomas Taimre & Philip K. Pollett, 2015. "Hawkes Processes," Papers 1507.02822, arXiv.org.
    9. BAUWENS, Luc & HAUTSCH, Nikolaus, 2006. "Modelling financial high frequency data using point processes," LIDAM Discussion Papers CORE 2006080, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    11. Anatoliy Swishchuk & Bruno Remillard & Robert Elliott & Jonathan Chavez-Casillas, 2017. "Compound Hawkes Processes in Limit Order Books," Papers 1712.03106, arXiv.org.
    12. Robert F. Engle & Asger Lunde, 2003. "Trades and Quotes: A Bivariate Point Process," Journal of Financial Econometrics, Oxford University Press, vol. 1(2), pages 159-188.
    13. Jonathan A. Ch'avez-Casillas & Robert J. Elliott & Bruno R'emillard & Anatoliy V. Swishchuk, 2017. "A level-1 Limit Order book with time dependent arrival rates," Papers 1704.06572, arXiv.org.
    14. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    15. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    16. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    17. Chavez-Demoulin, V. & McGill, J.A., 2012. "High-frequency financial data modeling using Hawkes processes," Journal of Banking & Finance, Elsevier, vol. 36(12), pages 3415-3426.
    18. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.
    19. Filimonov, Vladimir & Bicchetti, David & Maystre, Nicolas & Sornette, Didier, 2014. "Quantification of the high level of endogeneity and of structural regime shifts in commodity markets," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 174-192.
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    Cited by:

    1. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    2. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    3. Ana Roldan Contreras & Anatoliy Swishchuk, 2022. "Optimal Liquidation, Acquisition and Market Making Problems in HFT under Hawkes Models for LOB," Risks, MDPI, vol. 10(8), pages 1-32, August.
    4. Anatoliy Swishchuk, 2024. "Self-Exciting Random Evolutions (SEREs) and their Applications," Papers 2412.10592, arXiv.org.
    5. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, arXiv.org.
    6. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    7. Maxime Morariu-Patrichi & Mikko Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," CREATES Research Papers 2018-26, Department of Economics and Business Economics, Aarhus University.
    8. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.

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