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Extreme value models in a conditional duration intensity framework

  • Rodrigo Herrera
  • Bernhard Schipp
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    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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    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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    1. John Cotter & Kevin Dowd, 2011. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," Papers 1103.5653, arXiv.org.
    2. Alfonso Dufour & Robert F Engle, 2000. "The ACD Model: Predictability of the Time Between Concecutive Trades," ICMA Centre Discussion Papers in Finance icma-dp2000-05, Henley Business School, Reading University.
    3. Meitz, Mika & Teräsvirta, Timo, 2004. "Evaluating models of autoregressive conditional duration," SSE/EFI Working Paper Series in Economics and Finance 557, Stockholm School of Economics, revised 13 Dec 2004.
    4. BAUWENS, Luc & HAUTSCH, Nikolaus, . "Stochastic conditional intensity processes," CORE Discussion Papers RP -1937, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. 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.
    6. BAUWENS, Luc & GIOT, Pierre, . "The logarithmic ACD model: an application to the bid-ask quote process of three NYSE stocks," CORE Discussion Papers RP -1497, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
    8. 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.
    9. 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.
    10. 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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