DPOT Methodology: An Application to Value-at-Risk

  • M. I. Fraga Alves
  • P. Araújo Santos
Part of the Studies in Theoretical and Applied Statistics book series (STAS)


Threshold methods, based on fitting a stochastic model to the excesses over a threshold, were developed under the acronym POT (peaks over threshold). To eliminate the tendency to clustering of violations, a model-based approach within the POT framework, which uses the durations between excesses as covariates, is presented. Based on this approach we suggest models to forecast one-day-ahead Value-at-Risk and apply these models to the Standard & Poor’s 500 Index. Out of sample results provide evidence that they can perform better than state-of-the art risk models.


Generalize Pareto Distribution Independence Test Financial Time Series Extreme Value Theory Interval Forecast 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was partially supported by National Funds through FCT - Fundação para a Ciência e a Tecnologia, FCT//PTDC/MAT/101736/2008, EXTREMA project.


  1. 1.
    Araújo Santos, P., Fraga Alves, M.I.: VaR prediction with a duration based POT method. In: Proceedings of the ISF2010, 30th International Symposium on Forecasting, San Diego, CA (2010)Google Scholar
  2. 2.
    Araújo Santos, P., Fraga Alves, M.I.: A new class of independence tests for interval forecasts evaluation. Comput. Stat. Data Anal. 56, 3366–3380 (2012). doi:10.1016/j.csda2010.10.002Google Scholar
  3. 3.
    Balkema, A.A., de Haan, L.: Residual life time at great age. Ann. Probab. 2, 792–804 (1974)Google Scholar
  4. 4.
    Bekiros, S.D., Georgoutsos, D.A.: Estimation of value-at-risk by extreme value and conventional methods: a comparative evaluation of their predictive performance. J. Int. Financ. Markets Institut. Money 15(3), 2009–2228 (2005)Google Scholar
  5. 5.
    Berkowitz, J., Christoffersen P., Pelletier D.: Evaluating value-at-risk models with desk-level data. Management Science, Published online in Articles in Advance (2009)Google Scholar
  6. 6.
    Byström, H.: Managing extreme risks in tranquil and volatile markets using conditional extreme value theory. Int. Rev. Financ. Anal. 13, 133–152 (2004)Google Scholar
  7. 7.
    Christoffersen P.: Evaluating intervals forecasts. Int. Econ. Rev. 39, 841–862 (1998)Google Scholar
  8. 8.
    Diebold, F.X., Schuermann, T., Stroughair, J.D.: Pitfalls and opportunities in the use of extreme value theory in risk management. Working paper, Wharton School, University of Pennsylvania (1998), pp. 98–10Google Scholar
  9. 9.
    Embrechts, P., Klüppelberg, C., Mikosch, T.: Modeling Extremal Events for Insurance and Finance. Springer, Berlin (1997)Google Scholar
  10. 10.
    Engel, R.F., Manganelli, S.: CAViaR: conditional autoregressive value-at-risk by regression quantiles. J. Business Econ. Stat. 22, 367–381 (2004)Google Scholar
  11. 11.
    Ghorbel, A., Trabelsi, A.: Predictive performance of conditional extreme value theory in value-at-risk estimation. Int. J. Monet. Econ. Finance 1, 121–147 (2008)Google Scholar
  12. 12.
    Jorian, P.: Value at Risk: The New Benchmark for Managing Financial Risk. McGraw-Hill, New York (2000)Google Scholar
  13. 13.
    Kuester, K., Mittik, S., Paolella, M.S.: Value-at-risk prediction: a comparison of alternative strategies. J. Financ. Econometrics 4, 53–89 (2006)Google Scholar
  14. 14.
    Kupiec, P.: Techniques for verifying the accuracy of risk measurement models. J. Derivat. 3, 73–84 (1995)Google Scholar
  15. 15.
    McNeil, A.J., Frey, R.: Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. J. Empirical Finance 7, 271–300 (2000)Google Scholar
  16. 16.
    Ozun, A., Cifter, A., Yilmazer, S.: Filtered extreme value theory for value-at-risk estimation: evidence from Turkey. J. Risk Finance Incorporat. Balance Sheet 11, 164–179 (2010)Google Scholar
  17. 17.
    Pickands III, J.: Statistical inference using extreme value order statistics. Ann. Stat. 3, 119–131 (1975)Google Scholar
  18. 18.
    R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0, (2010)
  19. 19.
    Smith, R.: Estimating tails of probability distributions. Ann. Stat. 15, 1174–1207 (1987)Google Scholar
  20. 20.
    Smith, R.: Models for exceedances over high thresholds. J. R. Stat. Soc. B 52, 393–442 (1990)Google Scholar
  21. 21.
    Tsay, R.: Analysis of Financial Time Series. Wiley Series in Probability and Statistics, John Wiley & Sons (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculdade de Ciências, Departamento de Estatística e Investigação OperacionalUniversidade de LisboaLisboaPortugal
  2. 2.Instituto Politécnico de Santarém, Departamento de Informática e Métodos QuantitativosEscola Superior de Gestão e TecnologiaSantarémPortugal

Personalised recommendations