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Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations

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  • Anatoliy Swishchuk

    (University of Calgary)

Abstract

In this paper, we study 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 (LLNs) and Functional Central Limit Theorems (FCLTs), the main results of the present paper, for both cases, non-regime-switching (Lemma 1 and Theorem 1) and regime-switching (Lemma 2 and Theorem 2) cases. 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 investigating 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. Numerical examples are presented for LOBster and Cisco data.

Suggested Citation

  • Anatoliy Swishchuk, 2021. "Modelling of Limit Order Books by General Compound Hawkes Processes with Implementations," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 399-428, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09803-z
    DOI: 10.1007/s11009-020-09803-z
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    References listed on IDEAS

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    1. Ban Zheng & François Roueff & Frédéric Abergel, 2014. "Ergodicity and scaling limit of a constrained multivariate Hawkes process," Post-Print hal-00777941, HAL.
    2. 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.
    3. Anatoliy Swishchuk & Tyler Hofmeister & Katharina Cera & Julia Schmidt, 2017. "General Semi-Markov Model For Limit Order Books," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-21, May.
    4. 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.
    5. Luc, BAUWENS & Nikolaus, HAUTSCH, 2006. "Modelling Financial High Frequency Data Using Point Processes," Discussion Papers (ECON - Département des Sciences Economiques) 2006039, Université catholique de Louvain, Département des Sciences Economiques.
    6. 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.
    7. D’Amico, Guglielmo & Petroni, Filippo, 2018. "Copula based multivariate semi-Markov models with applications in high-frequency finance," European Journal of Operational Research, Elsevier, vol. 267(2), pages 765-777.
    8. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    9. 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.
    10. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    11. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Anatoliy Swishchuk, 2017. "Risk Model Based on General Compound Hawkes Process," Papers 1706.09038, arXiv.org.
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    Cited by:

    1. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, arXiv.org.
    2. Kyungsub Lee, 2023. "Multi-kernel property in high-frequency price dynamics under Hawkes model," Papers 2302.11822, arXiv.org.
    3. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-based Models," Papers 2104.02694, arXiv.org, revised May 2021.

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