IDEAS home Printed from https://ideas.repec.org/p/ces/ceswps/_6288.html
   My bibliography  Save this paper

How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?

Author

Listed:
  • Benjamin R. Auer
  • Benjamin Mögel

Abstract

In this study, we compare the out-of-sample forecasting performance of several modern Value-at- Risk (VaR) estimators derived from extreme value theory (EVT). Specifically, in a multi-asset study covering 30 years of stock, bond, commodity and currency market data, we analyse the accuracy of the classic generalised Pareto peak over threshold approach and three recently proposed methods based on the Box-Cox transformation, L-moment estimation and the Johnson system of distributions. We find that, in their unconditional form, some of the estimators are acceptable under current regulatory assessment rules but none of them can continuously pass more advanced tests of forecasting accuracy. In their conditional forms, forecasting power is significantly increased and the Box-Cox method proves to be the most promising estimator. However, it is also important to stress that the traditional historical simulation approach, which is currently the most frequently used VaR estimator in commercial banks, can not only keep up with the EVT-based methods but occasionally even outperforms them (depending on the setting: unconditional vs. conditional). Thus, recent claims to generally replace this simple method by theoretically more advanced EVT-based methods may be premature.

Suggested Citation

  • Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo Group Munich.
  • Handle: RePEc:ces:ceswps:_6288
    as

    Download full text from publisher

    File URL: http://www.cesifo-group.de/DocDL/cesifo1_wp6288.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Dirk G. Baur & Brian M. Lucey, 2010. "Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold," The Financial Review, Eastern Finance Association, vol. 45(2), pages 217-229, May.
    2. Ho, Lan-Chih & Burridge, Peter & Cadle, John & Theobald, Michael, 2000. "Value-at-risk: Applying the extreme value approach to Asian markets in the recent financial turmoil," Pacific-Basin Finance Journal, Elsevier, vol. 8(2), pages 249-275, May.
    3. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
    4. John Y. Campbell & Sanford J. Grossman & Jiang Wang, 1993. "Trading Volume and Serial Correlation in Stock Returns," The Quarterly Journal of Economics, Oxford University Press, vol. 108(4), pages 905-939.
    5. Martins-Filho Carlos & Yao Feng, 2006. "Estimation of Value-at-Risk and Expected Shortfall based on Nonlinear Models of Return Dynamics and Extreme Value Theory," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(2), pages 1-43, May.
    6. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    7. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
    8. Bali, Turan G., 2003. "The generalized extreme value distribution," Economics Letters, Elsevier, vol. 79(3), pages 423-427, June.
    9. Bianchi, Robert J. & Drew, Michael E. & Fan, John Hua, 2015. "Combining momentum with reversal in commodity futures," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 423-444.
    10. Brooks, C. & Clare, A.D. & Dalle Molle, J.W. & Persand, G., 2005. "A comparison of extreme value theory approaches for determining value at risk," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 339-352, March.
    11. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
    12. Gaglianone, Wagner Piazza & Lima, Luiz Renato & Linton, Oliver & Smith, Daniel R., 2011. "Evaluating Value-at-Risk Models via Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 150-160.
    13. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    14. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 53-89.
    15. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    16. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
    17. Carmen M. Reinhart & Kenneth S. Rogoff, 2009. "Is the 2007 U.S. Sub-Prime Financial Crisis So Different? An International Historical Comparison," Panoeconomicus, Savez ekonomista Vojvodine, Novi Sad, Serbia, vol. 56(3), pages 291-299, September.
    18. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 314-343, Spring.
    19. Baur, Dirk G. & McDermott, Thomas K., 2010. "Is gold a safe haven? International evidence," Journal of Banking & Finance, Elsevier, vol. 34(8), pages 1886-1898, August.
    20. repec:adr:anecst:y:2000:i:60 is not listed on IDEAS
    21. Soosung Hwang & Pedro L. Valls Pereira, 2006. "Small sample properties of GARCH estimates and persistence," The European Journal of Finance, Taylor & Francis Journals, vol. 12(6-7), pages 473-494.
    22. Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 997-1015, April.
    23. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 130-168.
    24. Fratzscher, Marcel, 2012. "Capital flows, push versus pull factors and the global financial crisis," Journal of International Economics, Elsevier, vol. 88(2), pages 341-356.
    25. Flannery, Mark J. & Kwan, Simon H. & Nimalendran, Mahendrarajah, 2013. "The 2007–2009 financial crisis and bank opaqueness," Journal of Financial Intermediation, Elsevier, vol. 22(1), pages 55-84.
    26. Elena-Ivona Dumitrescu & Christophe Hurlin & Vinson Pham, 2012. "Backtesting Value-at-Risk: From Dynamic Quantile to Dynamic Binary Tests," Finance, Presses universitaires de Grenoble, vol. 33(1), pages 79-112.
    27. Stijn Claessens & M. Ayhan Kose, 2013. "Financial Crises: Explanations, Types and Implications," CAMA Working Papers 2013-06, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    28. Marimoutou, Velayoudoum & Raggad, Bechir & Trabelsi, Abdelwahed, 2009. "Extreme Value Theory and Value at Risk: Application to oil market," Energy Economics, Elsevier, vol. 31(4), pages 519-530, July.
    29. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    30. Bali, Turan G. & Weinbaum, David, 2007. "A conditional extreme value volatility estimator based on high-frequency returns," Journal of Economic Dynamics and Control, Elsevier, vol. 31(2), pages 361-397, February.
    31. Danielsson, Jon & Morimoto, Yuji, 2000. "Forecasting Extreme Financial Risk: A Critical Analysis of Practical Methods for the Japanese Market," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 18(2), pages 25-48, December.
    32. El-Aroui, Mhamed-Ali & Diebolt, Jean, 2002. "On the use of the peaks over thresholds method for estimating out-of-sample quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 39(4), pages 453-475, June.
    33. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    34. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    35. Bali, Turan G. & Neftci, Salih N., 2003. "Disturbing extremal behavior of spot rate dynamics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 455-477, September.
    36. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    37. Cheng-Few Lee & Jung-Bin Su, 2012. "Alternative statistical distributions for estimating value-at-risk: theory and evidence," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 309-331, October.
    38. Carroll, Raymond J. & H rdle, Wolfgang & Mammen, Enno, 2002. "Estimation In An Additive Model When The Components Are Linked Parametrically," Econometric Theory, Cambridge University Press, vol. 18(04), pages 886-912, August.
    39. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-216, April.
    40. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    41. Giovanni Barone-Adesi & Kostas Giannopoulos, 2001. "Non parametric VaR Techniques. Myths and Realities," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 30(2), pages 167-181, July.
    42. Michael D. Bordo & John S. Landon-Lane, 2010. "The Global Financial Crisis of 2007-08: Is it Unprecedented?," NBER Working Papers 16589, National Bureau of Economic Research, Inc.
    43. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    44. Ziggel, Daniel & Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2014. "A new set of improved Value-at-Risk backtests," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 29-41.
    45. Pritsker, Matthew, 2006. "The hidden dangers of historical simulation," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 561-582, February.
    46. Pérignon, Christophe & Smith, Daniel R., 2010. "The level and quality of Value-at-Risk disclosure by commercial banks," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 362-377, February.
    47. Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2010. "The Use of GARCH Models in VaR Estimation," Working Papers 0048, University of Peloponnese, Department of Economics.
    48. Christophe Perignon & D. Smith, 2009. "The Level and Quality of Value-at-Risk Disclosure by Commercial Banks," Post-Print hal-00496102, HAL.
    49. repec:adr:anecst:y:2000:i:60:p:10 is not listed on IDEAS
    50. Marco Rocco, 2014. "Extreme Value Theory In Finance: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 28(1), pages 82-108, February.
    51. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    52. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annals of Economics and Statistics, GENES, issue 60, pages 239-270.
    53. Bartram, Söhnke M. & Bodnar, Gordon M., 2009. "No place to hide: The global crisis in equity markets in 2008/2009," Journal of International Money and Finance, Elsevier, vol. 28(8), pages 1246-1292, December.
    54. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
    55. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    56. Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    57. Tauchen, George, 2001. "Notes on financial econometrics," Journal of Econometrics, Elsevier, vol. 100(1), pages 57-64, January.
    58. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    59. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    60. Auer, Benjamin R., 2015. "Does the choice of performance measure influence the evaluation of commodity investments?," International Review of Financial Analysis, Elsevier, vol. 38(C), pages 142-150.
    61. Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 207-228, May.
    62. de Haan, L. & Pereira, T. Themido, 1999. "Estimating the index of a stable distribution," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 39-55, January.
    63. Taylor, Nick, 2014. "The rise and fall of technical trading rule success," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 286-302.
    64. Ciner, Cetin & Gurdgiev, Constantin & Lucey, Brian M., 2013. "Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates," International Review of Financial Analysis, Elsevier, vol. 29(C), pages 202-211.
    65. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    66. Yu Chuan Huang & Bor-Jing Lin, 2004. "Value-at-Risk Analysis for Taiwan Stock Index Futures: Fat Tails and Conditional Asymmetries in Return Innovations," Review of Quantitative Finance and Accounting, Springer, vol. 22(2), pages 79-95, March.
    67. Wong, Woon K., 2008. "Backtesting trading risk of commercial banks using expected shortfall," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1404-1415, July.
    68. Cheng, Wan-Hsiu & Hung, Jui-Cheng, 2011. "Skewness and leptokurtosis in GARCH-typed VaR estimation of petroleum and metal asset returns," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 160-173, January.
    69. Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
    70. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    71. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    72. Turan G. Bali, 2007. "A Generalized Extreme Value Approach to Financial Risk Measurement," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1613-1649, October.
    73. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    74. Hsieh, David A., 1993. "Implications of Nonlinear Dynamics for Financial Risk Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 28(01), pages 41-64, March.
    75. Bartram, Söhnke M. & Bodnar, Gordon M., 2009. "No Place To Hide: The Global Crisis in Equity Markets in 2008/09," MPRA Paper 15955, University Library of Munich, Germany.
    76. Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
    77. Itzhak Ben-David & Francesco Franzoni & Rabih Moussawi, 2012. "Hedge Fund Stock Trading in the Financial Crisis of 2007--2009," Review of Financial Studies, Society for Financial Studies, vol. 25(1), pages 1-54.
    78. Eli Ofek & Matthew Richardson, 2003. "DotCom Mania: The Rise and Fall of Internet Stock Prices," Journal of Finance, American Finance Association, vol. 58(3), pages 1113-1138, June.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    value-at-risk; extreme value theory; historical simulation; backtest; financial crisis;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ces:ceswps:_6288. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Klaus Wohlrabe). General contact details of provider: http://edirc.repec.org/data/cesifde.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.