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High-frequency financial data modeling using Hawkes processes

Author

Listed:
  • Chavez-Demoulin, V.
  • McGill, J.A.

Abstract

Intraday Value-at-Risk (VaR) is one of the risk measures used by market participants involved in high-frequency trading. High-frequency log-returns feature important kurtosis (fat tails) and volatility clustering (extreme log-returns appear in clusters) that VaR models should take into account. We propose a marked point process model for the excesses of the time series over a high threshold that combines Hawkes processes for the exceedances with a generalized Pareto distribution model for the marks (exceedance sizes). The conditional approach features intraday clustering of extremes and is used to calculate instantaneous conditional VaR. The models are backtested on real data and compared to a competitor approach that proposes a nonparametric extension of the classical peaks-over-threshold method. Maximum likelihood estimation is computationally intensive; we use a differential evolution genetic algorithm to find adequate starting values for the optimization process.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jbfina:v:36:y:2012:i:12:p:3415-3426
    DOI: 10.1016/j.jbankfin.2012.08.011
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    References listed on IDEAS

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    1. Dionne, Georges & Duchesne, Pierre & Pacurar, Maria, 2009. "Intraday Value at Risk (IVaR) using tick-by-tick data with application to the Toronto Stock Exchange," Journal of Empirical Finance, Elsevier, vol. 16(5), pages 777-792, December.
    2. Pierre Giot, 2005. "Market risk models for intraday data," The European Journal of Finance, Taylor & Francis Journals, vol. 11(4), pages 309-324.
    3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    4. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    5. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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    Citations

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    Cited by:

    1. Clements, A.E. & Herrera, R. & Hurn, A.S., 2015. "Modelling interregional links in electricity price spikes," Energy Economics, Elsevier, vol. 51(C), pages 383-393.
    2. repec:oup:jfinec:v:15:y:2017:i:1:p:139-171. is not listed on IDEAS
    3. Chavez-Demoulin, V. & Embrechts, P. & Sardy, S., 2014. "Extreme-quantile tracking for financial time series," Journal of Econometrics, Elsevier, vol. 181(1), pages 44-52.
    4. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.
    5. Hainaut, Donatien, 2016. "Impact of volatility clustering on equity indexed annuities," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 367-381.
    6. Anatoliy Swishchuk, 2017. "General Compound Hawkes Processes in Limit Order Books," Papers 1706.07459, arXiv.org, revised Jun 2017.
    7. Herrera, Rodrigo & Schipp, Bernhard, 2014. "Statistics of extreme events in risk management: The impact of the subprime and global financial crisis on the German stock market," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 218-238.
    8. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Specification Testing in Hawkes Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 15(1), pages 139-171.
    9. Herrera, Rodrigo & González, Nicolás, 2014. "The modeling and forecasting of extreme events in electricity spot markets," International Journal of Forecasting, Elsevier, vol. 30(3), pages 477-490.
    10. Fernanda Fuentes & Rodrigo Herrera & Adam Clements, 2016. "Modelling Extreme Risks in Commodities and Commodity Currencies," NCER Working Paper Series 115, National Centre for Econometric Research.
    11. Gresnigt, Francine & Kole, Erik & Franses, Philip Hans, 2015. "Interpreting financial market crashes as earthquakes: A new Early Warning System for medium term crashes," Journal of Banking & Finance, Elsevier, vol. 56(C), pages 123-139.
    12. Wheatley, Spencer & Filimonov, Vladimir & Sornette, Didier, 2016. "The Hawkes process with renewal immigration & its estimation with an EM algorithm," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 120-135.
    13. Anatoliy Swishchuk & Bruno Remillard & Robert Elliott & Jonathan Chavez-Casillas, 2017. "Compound Hawkes Processes in Limit Order Books," Papers 1712.03106, arXiv.org.
    14. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.
    15. Karmakar, Madhusudan & Paul, Samit, 2016. "Intraday risk management in International stock markets: A conditional EVT approach," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 34-55.
    16. Herrera, Rodrigo, 2013. "Energy risk management through self-exciting marked point process," Energy Economics, Elsevier, vol. 38(C), pages 64-76.
    17. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    18. repec:eee:eneeco:v:63:y:2017:i:c:p:129-143 is not listed on IDEAS
    19. Donatien Hainaut, 2016. "A bivariate Hawkes process based model, for interest rates," Post-Print hal-01458162, HAL.
    20. Donatien Hainaut, 2016. "A model for interest rates with clustering effects," Post-Print hal-01393994, HAL.
    21. Grothe, Oliver & Korniichuk, Volodymyr & Manner, Hans, 2014. "Modeling multivariate extreme events using self-exciting point processes," Journal of Econometrics, Elsevier, vol. 182(2), pages 269-289.
    22. Angelos Dassios & Hongbiao Zhao, 2014. "A Markov Chain Model for Contagion," Risks, MDPI, Open Access Journal, vol. 2(4), pages 1-22, November.
    23. Dassios, Angelos & Zhao, Hongbiao, 2014. "A Markov chain model for contagion," LSE Research Online Documents on Economics 60155, London School of Economics and Political Science, LSE Library.

    More about this item

    Keywords

    Hawkes process; High-frequency data; Peaks-over-threshold; Self-exciting process; Value-at-risk;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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