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Conditional EVT for VAR Estimation: Comparison with a New Independence Test

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Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

Abstract

We compare the out-of-sample performance of methods for value-at-risk (VaR) estimation, using a new exact independence test. This test is appropriate for detecting risk models with a tendency to generate clusters of violations and evaluating the performance under heteroscedastic time series. We focus the comparison on a two-stage hybrid method which combines a GARCH filter with an extreme value theory (EVT) approach, known as conditional EVT. Previous comparative studies show that this method performs better for VaR estimation. Our contributions are comparing the performance with the new exact independence test and considering recent developments in EVT involving bias reduction.

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References

  1. Araújo Santos, P., Fraga Alves, M.I.: A new class of independence tests for interval forecasts evaluation. Computational Statistics and Data Analysis, 56(11), 3366–3380 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  2. Balkema, A.A. e de Haan, L.: Residual life time at great age. Ann. Probab. 2, 792–804 (1974)

    Google Scholar 

  3. Barone-Adesi, G., Bourgoin, F., Giannopoulos, K.: Dont look back. Risk 11(8), 100–103 (1998)

    Google Scholar 

  4. Basel Committee on Banking Supervision: Supervisory Framework for the Use of Back- testing in Conjunction with the Internal Model-Based Approach to Market Risk Capital Requirements. BIS, Basel, Switzerland (1996)

    Google Scholar 

  5. Beirlant, J., Dierckx, G., Goegebeur, Y., Matthys, G.: Tail index estimation and exponential regression model. Extremes 2, 177–200 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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. Market. Inst. Money 15(3), 209–228 (2005)

    Article  Google Scholar 

  7. Bystrom, H.: Managing extreme risks in tranquil and volatile markets using conditional extreme value theory. Int. Rev. Financ. Anal. 13, 133–152 (2004)

    Article  Google Scholar 

  8. Caeiro, F., Gomes, M.I.: A class of asymptotically unbiased semi-parametric estimators of the tail index. Test 11(2), 345–364 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Caeiro, F., Gomes, M.I., Pestana, D.: Direct reduction of bias of the classical Hill estimator. RevStat 3(2), 111–136 (2005)

    MathSciNet  Google Scholar 

  10. Christoffersen, P.: Evaluating intervals forecasts. Int. Econ. Rev. 39, 841–862 (1998)

    Article  MathSciNet  Google Scholar 

  11. Diebold, F.X., Schuermann, T., Stroughair, J.D.: Pitfalls and opportunities in the use of extreme value theory in risk management. In: Working Paper, pp. 98–10, Wharton School, University of Pennsylvania (1998)

    Google Scholar 

  12. Fernandez, C., Steel, M.F.J.: On Bayesian modelling of fat tails and skewness. J. Am. Stat. Assoc. 93, 359–371 (1998)

    MathSciNet  MATH  Google Scholar 

  13. Fraga Alves, M.I., Gomes, M.I., de Haan, L.: A new class of semi-parametric estimators of the second order parameter. Portugaliae Mathematica 60(1), 193–213 (2003)

    MathSciNet  MATH  Google Scholar 

  14. Ghorbel, A., Trabelsi, A.: Predictive performance of conditional extreme value theory in value-at-risk estimation. Int. J. Monetary Econ. Finance. 1(2), 121–147 (2008)

    Article  Google Scholar 

  15. Giot, P., Laurent, S.: Modelling daily value-at-risk using realized volatility and ARCH type models. J. Empir. Finance 11, 379–398 (2004)

    Article  Google Scholar 

  16. Gomes, M.I., Martins, M.J., Neves M.M.: Alternatives to a semi-parametric estimator of parameters of rare events - the Jackknife methodology. Extremes 3(3), 207–229 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  17. Gomes, M.I., Martins, M.J., Neves M.M.: Generalized Jackknife semi-parametric estimators of the tail index. Portugaliae Mathematics 59(4), 393–408 (2002)

    MathSciNet  MATH  Google Scholar 

  18. Gomes, M.I., Martins, M.J.: Asymptotically unbiased estimators of the tail index based on the external estimation of the second order parameter. Extremes 5(1), 5–31 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  19. Gomes, M.I., Pestana D.: A sturdy reduced bias extreme quantile (VaR) estimator. J. Am. Statist. Assoc. 102(477), 280–292 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  20. Gomes, M.I., Martins, M.J., Neves, M.M.: Improving second order reduced-bias tail index estimator. Revstat 5(2), 177–207 (2007)

    MathSciNet  MATH  Google Scholar 

  21. Gomes, M.I., de Haan, L., Henriques Rodrigues, L.: Tail Index estimation for heavy-tailed models: accommodation of bias in weighted log-excesses. J. Roy. Stat. Soc. B70(1), 31–52 (2008)

    Google Scholar 

  22. Hill, B.M.: A simple general approach to inference about the tail of a distribution. Ann. Statist. 3(5), 1163–1174 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  23. Jorian, P.: Value at Risk: The New Benchmark for Managing Financial Risk. McGraw- Hill, New York (2000)

    Google Scholar 

  24. Kuester, K., Mittik, S., Paolella, M.S.: Value-at-risk prediction: a comparison of alternative strategies. J. Financ. Econometrics 4(1), 53–89 (2006)

    Article  Google Scholar 

  25. Kupiec, P.: Techniques for verifying the accuracy of risk measurement models. J. Deriv. 3, 73–84 (1995)

    Article  Google Scholar 

  26. McNeil, A.J., Frey, R.: Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach. J. Empir. Finance 7, 271–300 (2000)

    Article  Google Scholar 

  27. Mittnik, S., Paolella, M.S.: Conditional density and value-at-risk prediction of asian currency exchange rates. J. Forecast. 19, 313–333 (2000)

    Article  Google Scholar 

  28. Peng, L.: Asymptotically unbiased estimator for the extreme-value-index. Stat. Probab. Lett. 38(2), 107–115 (1998)

    Article  MATH  Google Scholar 

  29. Pickands III, J.: Statistical inference using extreme value order statistics. Ann. Statist. 3, 119–131 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  30. R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http://www.R-project.org(2008)

  31. Ribatet, M.: POT: Generalized Pareto Distribution and Peaks Over Threshold. R package version 1.0–9. http://people.epf1.ch/mathieu.ribatet, http://r-forge.r-project.org/projects/pot/ (2009)

  32. Weissman, I.: Estimation of parameters and large quantiles based on the k largest observations. J. Am. Stat. Assoc. 73, 812–815 (1978)

    MathSciNet  MATH  Google Scholar 

  33. Wuertz, D., Chalabi, Y., Miklovic M.: fGarch: Rmetrics - Autoregressive Conditional Heteroskedastic Modelling, R package version 290.76. http://www.rmetrics.org (2008)

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Acknowledgements

Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, FCT/PROTEC, project PEst-OE/MAT/UI0006/2011, and FCT /PTDC/MAT/101736/2008, EXTREMA project. The authors would like to thank the two referees for their comments and suggestions which lead to improvements of an earlier version of this chapter.

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Authors and Affiliations

  1. Departamento de Estatística e Investigação Operacional, Universidade de Lisboa, Lisboa, Portugal

    M. I. Fraga Alves

  2. CEAUL, Lisboa, Portugal

    M. I. Fraga Alves & P. Araújo Santos

  3. Departamento de Informática e Métodos Quantitativos, Escola Superior de Gestão e Tecnologia, Instituto Politécnico de Santarém, Lisboa, Portugal

    P. Araújo Santos

Authors
  1. M. I. Fraga Alves
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  2. P. Araújo Santos
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Corresponding author

Correspondence to M. I. Fraga Alves .

Editor information

Editors and Affiliations

  1. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    João Lita da Silva

  2. , Universidade Nova de Lisboa, CMA and Faculdade de Ciˆenciase Tecnolog, Caparica, Caparica, 2829-516, Portugal

    Frederico Caeiro

  3. , Universidade Nova de Lisboa, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica, Caparica, 2829-516, Portugal

    Isabel Natário

  4. , Universidade Nova de Lisboa,, CEAUL and Faculdade de Ciˆenciase Tecnol, Caparica 59, Caparica, 2829-516, Portugal

    Carlos A. Braumann

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Alves, M.I.F., Santos, P.A. (2013). Conditional EVT for VAR Estimation: Comparison with a New Independence Test. In: Lita da Silva, J., Caeiro, F., Natário, I., Braumann, C. (eds) Advances in Regression, Survival Analysis, Extreme Values, Markov Processes and Other Statistical Applications. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34904-1_19

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