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Extreme value models in a conditional duration intensity framework

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  • Rodrigo Herrera
  • Bernhard Schipp
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    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.

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    File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2011-022.pdf
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    Bibliographic Info

    Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2011-022.

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    Length: 34 pages
    Date of creation: May 2011
    Date of revision:
    Handle: RePEc:hum:wpaper:sfb649dp2011-022

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

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    References

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    1. Alfonso Dufour & Robert F Engle, 2000. "The ACD Model: Predictability of the Time Between Concecutive Trades," ICMA Centre Discussion Papers in Finance, Henley Business School, Reading University icma-dp2000-05, Henley Business School, Reading University.
    2. Meitz, Mika & Terasvirta, Timo, 2006. "Evaluating Models of Autoregressive Conditional Duration," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 24, pages 104-124, January.
    3. Luc BAUWENS & Pierre GIOT, 2000. "The Logarithmic ACD Model: An Application to the Bid-Ask Quote Process of Three NYSE Stocks," Annales d'Economie et de Statistique, ENSAE, issue 60, pages 117-149.
    4. Joachim Grammig & Kai-Oliver Maurer, 2000. "Non-monotonic hazard functions and the autoregressive conditional duration model," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 3(1), pages 16-38.
    5. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, Econometric Society, vol. 66(5), pages 1127-1162, September.
    6. 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.
    7. Jon DANIELSSON & Casper G. DE VRIES, 2000. "Value-at-Risk and Extreme Returns," Annales d'Economie et de Statistique, ENSAE, issue 60, pages 239-270.
    8. BAUWENS, Luc & HAUTSCH, Nikolaus, . "Stochastic conditional intensity processes," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1937, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. John Cotter & Kevin Dowd, 2011. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," Papers 1103.5653, arXiv.org.
    10. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
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