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Extreme value models in a conditional duration intensity framework

Author

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  • Rodrigo Herrera
  • Bernhard Schipp

Abstract

The analysis of return series from financial markets is often based on the Peaks-over-threshold (POT) model. This model assumes independent and identically distributed observations and therefore a Poisson process is used to characterize the occurrence of extreme events. However, stylized facts such as clustered extremes and serial dependence typically violate the assumption of independence. In this paper we concentrate on an alternative approach to overcome these difficulties. We consider the stochastic intensity of the point process of exceedances over a threshold in the framework of irregularly spaced data. The main idea is to model the time between exceedances through an Autoregressive Conditional Duration (ACD) model, while the marks are still being modelled by generalized Pareto distributions. The main advantage of this approach is its capability to capture the short-term behaviour of extremes without involving an arbitrary stochastic volatility model or a prefiltration of the data, which certainly impacts the estimation. We make use of the proposed model to obtain an improved estimate for the Value at Risk. The model is then applied and illustrated to transactions data from Bayer AG, a blue chip stock from the German stock market index DAX.

Suggested Citation

  • Rodrigo Herrera & Bernhard Schipp, 2011. "Extreme value models in a conditional duration intensity framework," SFB 649 Discussion Papers SFB649DP2011-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  • Handle: RePEc:hum:wpaper:sfb649dp2011-022
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
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    6. Meitz, Mika & Terasvirta, Timo, 2006. "Evaluating Models of Autoregressive Conditional Duration," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 104-124, January.
    7. Joachim Grammig & Kai-Oliver Maurer, 2000. "Non-monotonic hazard functions and the autoregressive conditional duration model," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 16-38.
    8. Paul Embrechts, 2009. "Linear Correlation and EVT: Properties and Caveats," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 7(1), pages 30-39, Winter.
    9. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
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    Citations

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    Cited by:

    1. Chen, Ray-Bing & Chen, Ying & Härdle, Wolfgang K., 2014. "TVICA—Time varying independent component analysis and its application to financial data," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 95-109.
    2. Sven Tischer & Lutz Hildebrandt, 2011. "Linking corporate reputation and shareholder value using the publication of reputation rankings," SFB 649 Discussion Papers SFB649DP2011-065, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Gökhan Cebiroğlu & Ulrich Horst, 2011. "Optimal Display of Iceberg Orders," SFB 649 Discussion Papers SFB649DP2011-057, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Luc Bauwens & Christian M. Hafner & Diane Pierret, 2013. "Multivariate Volatility Modeling Of Electricity Futures," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(5), pages 743-761, August.
    5. Patrick Cheridito & Ulrich Horst & Michael Kupper & Traian A. Pirvu, 2016. "Equilibrium Pricing in Incomplete Markets Under Translation Invariant Preferences," Mathematics of Operations Research, INFORMS, vol. 41(1), pages 174-195, February.
    6. Raffaele Fiocco, 2012. "Competition and regulation with product differentiation," Journal of Regulatory Economics, Springer, vol. 42(3), pages 287-307, December.
    7. Bocart, Fabian Y.R.P. & Hafner, Christian M., 2012. "Econometric analysis of volatile art markets," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3091-3104.
    8. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(05), pages 1140-1177, October.
    9. Gökhan Cebiro˜glu & Ulrich Horst, 2011. "Optimal liquidation in dark pools," SFB 649 Discussion Papers SFB649DP2011-058, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    10. Nikolaus Hautsch & Julia Schaumburg & Melanie Schienle, 2015. "Financial Network Systemic Risk Contributions," Review of Finance, European Finance Association, vol. 19(2), pages 685-738.
    11. Wolfgang Härdle & Maria Osipenko, 2011. "Pricing Chinese rain: a multi-site multi-period equilibrium pricing model for rainfall derivatives," SFB 649 Discussion Papers SFB649DP2011-055, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    12. Alena MyÅ¡iÄ ková & Song Song & Piotr Majer & Peter N.C. Mohr & Hauke R. Heekeren & Wolfgang K. Härdle, 2011. "Risk Patterns and Correlated Brain Activities. Multidimensional statistical analysis of fMRI data with application to risk patterns," SFB 649 Discussion Papers SFB649DP2011-085, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Dorothee Schneider, 2011. "The Labor Share: A Review of Theory and Evidence," SFB 649 Discussion Papers SFB649DP2011-069, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    14. Nikolaus Hautsch & Ruihong Huang, 2011. "Limit Order Flow, Market Impact and Optimal Order Sizes: Evidence from NASDAQ TotalView-ITCH Data," SFB 649 Discussion Papers SFB649DP2011-056, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    15. Aurélie Bertrand & Christian Hafner, 2014. "On heterogeneous latent class models with applications to the analysis of rating scores," Computational Statistics, Springer, vol. 29(1), pages 307-330, February.
    16. Gregor Heyne & Michael Kupper & Christoph Mainberger, 2011. "Minimal Supersolutions of BSDEs with Lower Semicontinuous Generators," SFB 649 Discussion Papers SFB649DP2011-067, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    17. Ulrich Horst & Michael Kupper & Andrea Macrina & Christoph Mainberger, 2011. "Continuous Equilibrium under Base Preferences and Attainable Initial Endowments," SFB 649 Discussion Papers SFB649DP2011-082, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Extreme value theory; autoregressive conditional duration; value at risk; self-exciting; point process; conditional intensity;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • F30 - International Economics - - International Finance - - - General

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