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Quantitative and Comparative Analyses of Limit Order Books with General Compound Hawkes Processes

Author

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  • Qiyue He

    (Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N1N4, Canada)

  • Anatoliy Swishchuk

    (Department of Mathematics and Statistics, University of Calgary, 2500 University Drive NW, Calgary, AB T2N1N4, Canada)

Abstract

In this paper, we solve the problem of mid price movements arising in high-frequency and algorithmic trading using real data. Namely, we introduce different new types of General Compound Hawkes Processes (GCHPDO, GCHP2SDO, GCHPnSDO) and find their diffusive limits to model the mid price movements of 6 stocks-EBAY, FB, MU, PCAR, SMH, CSCO. We also define error rates to estimate the models fitting accuracy. Maximum Likelihood Estimation (MLE) and Particle Swarm Optimization (PSO) are used for Hawkes processes and models parameters’ calibration.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jrisks:v:7:y:2019:i:4:p:110-:d:282628
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    References listed on IDEAS

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    1. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    2. Bacry, E. & Delattre, S. & Hoffmann, M. & Muzy, J.F., 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2475-2499.
    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. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    5. Patrick J. Laub & Thomas Taimre & Philip K. Pollett, 2015. "Hawkes Processes," Papers 1507.02822, arXiv.org.
    6. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    7. Jonathan A. Chávez-Casillas & Robert J. Elliott & Bruno Rémillard & Anatoliy V. Swishchuk, 2019. "A Level-1 Limit Order Book with Time Dependent Arrival Rates," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 699-719, September.
    8. Anatoliy Swishchuk & Aiden Huffman, 2018. "General Compound Hawkes Processes in Limit Order Books," Papers 1812.02298, arXiv.org.
    9. Stéphane Goutte & David Guerreiro & Bilel Sanhaji & Sophie Saglio & Julien Chevallier, 2019. "Financial Mathematics, Volatility and Covariance Modelling," Post-Print halshs-02183052, HAL.
    10. Emmanuel Bacry & Sylvain Delattre & Marc Hoffmann & Jean-François Muzy, 2013. "Some limit theorems for Hawkes processes and application to financial statistics," Post-Print hal-01313994, HAL.
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    Citations

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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. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, 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.
    4. Anatoliy Swishchuk, 2021. "Merton Investment Problems in Finance and Insurance for the Hawkes-Based Models," Risks, MDPI, vol. 9(6), pages 1-13, June.

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