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Extreme value theory for finance: a survey

  • Marco Rocco

    ()

    (Banca d'Italia)

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    Extreme value theory is concerned with the study of the asymptotical distribution of extreme events, that is to say events which are rare in frequency and huge with respect to the majority of observations. Statistical methods derived from this theory have been increasingly employed in finance, especially in the context of risk measurement. The aim of the present study is twofold. The first part delivers a critical review of the theoretical underpinnings of extreme value theory. The second part provides a survey of some major applications of extreme value theory to finance, namely its use to test different distributional assumptions for the data, Value-at-Risk and Expected Shortfall calculations, asset allocation under safety-first type constraints and the study of contagion and dependence across markets under stress conditions.

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    Paper provided by Bank of Italy, Economic Research and International Relations Area in its series Questioni di Economia e Finanza (Occasional Papers) with number 99.

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    Date of creation: Jul 2011
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    Handle: RePEc:bdi:opques:qef_99_11
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    1. Turan G. Bali & Salih N. Neftci, 2002. "Disturbing Extremal Behavior of Spot Rate Dynamics," ICMA Centre Discussion Papers in Finance icma-dp2002-03, Henley Business School, Reading University.
    2. Jansen, Dennis W. & Koedijk, Kees G. & de Vries, Casper G., 2000. "Portfolio selection with limited downside risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 247-269, November.
    3. Hyung, Namwon & de Vries, Casper G., 2007. "Portfolio selection with heavy tails," Journal of Empirical Finance, Elsevier, vol. 14(3), pages 383-400, June.
    4. Cotter, JOhn & Dowd, Kevin, 2006. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," MPRA Paper 3505, University Library of Munich, Germany.
    5. John Cotter, 2011. "Varying the VaR for Unconditional and Conditional Environments," Papers 1103.5649, arXiv.org.
    6. Danielsson, Jon & Jorgensen, Bjorn N. & Sarma, Mandira & de Vries, Casper G., 2006. "Comparing downside risk measures for heavy tailed distributions," Economics Letters, Elsevier, vol. 92(2), pages 202-208, August.
    7. Bystrom, Hans N. E., 2004. "Managing extreme risks in tranquil and volatile markets using conditional extreme value theory," International Review of Financial Analysis, Elsevier, vol. 13(2), pages 133-152.
    8. Quintos, Carmela & Fan, Zhenhong & Phillips, Peter C B, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," Review of Economic Studies, Wiley Blackwell, vol. 68(3), pages 633-63, July.
    9. 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.).
    10. Jan P. A. M. Lestano, 2007. "Dating currency crises with ad hoc and extreme value-based thresholds: East Asia 1970-2002 [Dating currency crises]," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 12(4), pages 371-388.
    11. Christopher A. T. Ferro & Johan Segers, 2003. "Inference for clusters of extreme values," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 545-556.
    12. repec:ner:tilbur:urn:nbn:nl:ui:12-3108712 is not listed on IDEAS
    13. Gus Garita & Chen Zhou, 2009. "Can Open Capital Markets Help Avoid Currency Crises?," DNB Working Papers 205, Netherlands Central Bank, Research Department.
    14. Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-16, April.
    15. Andreas Jobst, 2007. "Operational Risk; The Sting is Still in the Tail But the Poison Dependson the Dose," IMF Working Papers 07/239, International Monetary Fund.
    16. Timotheos Angelidis & Alexandros Benos & Stavros Degiannakis, 2007. "A robust VaR model under different time periods and weighting schemes," Review of Quantitative Finance and Accounting, Springer, vol. 28(2), pages 187-201, February.
    17. H. A. Hauksson & M. Dacorogna & T. Domenig & U. Mller & G. Samorodnitsky, 2001. "Multivariate extremes, aggregation and risk estimation," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 79-95.
    18. 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.
    19. Arzac, Enrique R. & Bawa, Vijay S., 1977. "Portfolio choice and equilibrium in capital markets with safety-first investors," Journal of Financial Economics, Elsevier, vol. 4(3), pages 277-288, May.
    20. Stelios Bekiros & Dimitris Georgoutsos, 2007. "Extreme returns and the contagion effect between the foreign exchange and the stock market: evidence from Cyprus," Applied Financial Economics, Taylor & Francis Journals, vol. 18(3), pages 239-254.
    21. Fong Chan, Kam & Gray, Philip, 2006. "Using extreme value theory to measure value-at-risk for daily electricity spot prices," International Journal of Forecasting, Elsevier, vol. 22(2), pages 283-300.
    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. Cotter, John, 2007. "Extreme risk in Asian equity markets," MPRA Paper 3536, University Library of Munich, Germany.
    24. Chapelle, Ariane & Crama, Yves & Hübner, Georges & Peters, Jean-Philippe, 2008. "Practical methods for measuring and managing operational risk in the financial sector: A clinical study," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1049-1061, June.
    25. John Cotter, 2005. "Extreme risk in futures contracts," Applied Economics Letters, Taylor & Francis Journals, vol. 12(8), pages 489-492.
    26. Jon Vilasuso & David Katz, 2000. "Estimates of the likelihood of extreme returns in international stock markets," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(1), pages 119-130.
    27. Hartmann, Philipp & Straetmans, Stefan & de Vries, Casper, 2001. "Asset market linkages in crisis periods," Working Paper Series 0071, European Central Bank.
    28. Victor Pontines & Reza Siregar, 2006. "Fundamental Pitfalls of Exchange Market Pressure-Based Approaches to Identification of Currency Crises," Centre for International Economic Studies Working Papers 2006-02, University of Adelaide, Centre for International Economic Studies.
    29. Lux, T., . "The Limiting Extremal Behaviour of Speculative Returns: An Analysis of Intra-Daily Data from the Frankfurt Stock Exchange," Discussion Paper Serie B 436, University of Bonn, Germany, revised Jul 1998.
    30. Bekiros, Stelios D. & Georgoutsos, Dimitris A., 2008. "The extreme-value dependence of Asia-Pacific equity markets," Journal of Multinational Financial Management, Elsevier, vol. 18(3), pages 197-208, July.
    31. Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
    32. Novak, S.Y. & Beirlant, J., 2006. "The magnitude of a market crash can be predicted," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 453-462, February.
    33. 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.
    34. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
    35. Bekiros, Stelios D. & Georgoutsos, Dimitris A., 2005. "Estimation of Value-at-Risk by extreme value and conventional methods: a comparative evaluation of their predictive performance," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 15(3), pages 209-228, July.
    36. 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.
    37. Hsieh, Ping-Hung, 2001. "Modelling the Frequency and Severity of Extreme Exchange Rate Returns," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(7), pages 485-99, November.
    38. Bali, Turan G., 2003. "The generalized extreme value distribution," Economics Letters, Elsevier, vol. 79(3), pages 423-427, June.
    39. Hartmann, Philipp & Straetmans, Stefan & de Vries, Casper, 2005. "Banking system stability: a cross-Atlantic perspective," Working Paper Series 0527, European Central Bank.
    40. Viviana Fernández, 2003. "Extreme Value Theory and Value at Risk," Documentos de Trabajo 154, Centro de Economía Aplicada, Universidad de Chile.
    41. Konstantinos Tolikas & Athanasios Koulakiotis & Richard A. Brown, 2007. "Extreme Risk and Value-at-Risk in the German Stock Market," The European Journal of Finance, Taylor & Francis Journals, vol. 13(4), pages 373-395.
    42. Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Society for Computational Economics, vol. 27(2), pages 207-228, May.
    43. Tai-Kuang Ho, 2008. "Extremal analysis of currency crises in Taiwan," Applied Economics, Taylor & Francis Journals, vol. 40(9), pages 1175-1186.
    44. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    45. Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
    46. Zhou, Chen, 2009. "Existence and consistency of the maximum likelihood estimator for the extreme value index," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 794-815, April.
    47. Upper, Christian & Werner, Thomas, 2002. "Time variation in the tail behaviour of bunds futures returns," Working Paper Series 0199, European Central Bank.
    48. 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 841-62, November.
    49. Cotter, John, 2001. "Margin exceedences for European stock index futures using extreme value theory," Journal of Banking & Finance, Elsevier, vol. 25(8), pages 1475-1502, August.
    50. 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.
    51. Gupta, Anurag & Liang, Bing, 2005. "Do hedge funds have enough capital? A value-at-risk approach," Journal of Financial Economics, Elsevier, vol. 77(1), pages 219-253, July.
    52. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
    53. Jorge A. Chan-Lau & Srobona Mitra & Li L. Ong, 2007. "Contagion Risk in the International Banking System and Implications for London As a Global Financial Center," IMF Working Papers 07/74, International Monetary Fund.
    54. Marco Moscadelli, 2004. "The modelling of operational risk: experience with the analysis of the data collected by the Basel Committee," Temi di discussione (Economic working papers) 517, Bank of Italy, Economic Research and International Relations Area.
    55. John Cotter, 2004. "Downside risk for European equity markets," Applied Financial Economics, Taylor & Francis Journals, vol. 14(10), pages 707-716.
    56. Hans Bystrom, 2006. "Using extreme value theory to estimate the likelihood of banking sector failure," The European Journal of Finance, Taylor & Francis Journals, vol. 12(4), pages 303-312.
    57. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
    58. Thomas Werner & Christian Upper, 2004. "Time variation in the tail behavior of Bund future returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 24(4), pages 387-398, 04.
    59. Byström, Hans, 2001. "Extreme Value Theory and Extremely Large Electricity Price Changes," Working Papers 2001:19, Lund University, Department of Economics.
    60. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420.
    61. Thierry Ané, 2006. "Two-Component Extreme Value Distribution For Asia-Pacific Stock Index Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(05), pages 643-671.
    62. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    63. Jondeau, Eric & Rockinger, Michael, 2003. "Testing for differences in the tails of stock-market returns," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 559-581, December.
    64. Hans Dewachter & Geert Gielens, 1999. "Setting futures margins: the extremes approach," Applied Financial Economics, Taylor & Francis Journals, vol. 9(2), pages 173-181.
    65. Haile, Fasika & Pozo, Susan, 2008. "Currency crisis contagion and the identification of transmission channels," International Review of Economics & Finance, Elsevier, vol. 17(4), pages 572-588, October.
    66. Zhou, Chen, 2010. "The extent of the maximum likelihood estimator for the extreme value index," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 971-983, April.
    67. Pearson, Neil D. & Smithson, Charles, 2002. "VaR: The state of play," Review of Financial Economics, Elsevier, vol. 11(3), pages 175-189.
    68. repec:dgr:kubcen:200929 is not listed on IDEAS
    69. Fasika Damte Haile & Susan Pozo, 2006. "Exchange Rate Regimes and Currency Crises: an Evaluation using Extreme Value Theory," Review of International Economics, Wiley Blackwell, vol. 14(4), pages 554-570, 09.
    70. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    71. 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.
    72. Pozo, Susan & Amuedo-Dorantes, Catalina, 2003. "Statistical distributions and the identification of currency crises," Journal of International Money and Finance, Elsevier, vol. 22(4), pages 591-609, August.
    73. Zhou, Chen, 2010. "Dependence structure of risk factors and diversification effects," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 531-540, June.
    74. Juri, Alessandro & Wuthrich, Mario V., 2002. "Copula convergence theorems for tail events," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 405-420, June.
    75. Jalal, Amine & Rockinger, Michael, 2008. "Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 868-877, December.
    76. Krehbiel, Tim & Adkins, Lee C., 2008. "Extreme daily changes in U.S. Dollar London inter-bank offer rates," International Review of Economics & Finance, Elsevier, vol. 17(3), pages 397-411.
    77. Koedijk, Kees G. & Stork, Philip A. & de Vries, Casper G., 1992. "Differences between foreign exchange rate regimes: The view from the tails," Journal of International Money and Finance, Elsevier, vol. 11(5), pages 462-473, October.
    78. Ulf Nielsson, 2009. "Measuring and regulating extreme risk," Journal of Financial Regulation and Compliance, Emerald Group Publishing, vol. 17(2), pages 156-171, May.
    79. Allen, Linda & Bali, Turan G., 2007. "Cyclicality in catastrophic and operational risk measurements," Journal of Banking & Finance, Elsevier, vol. 31(4), pages 1191-1235, April.
    80. Pontines, Victor & Siregar, Reza, 2007. "The Yen, the US dollar, and the trade weighted basket of currencies: Does the choice of anchor currencies matter in identifying incidences of speculative attacks?," Japan and the World Economy, Elsevier, vol. 19(2), pages 214-235, March.
    81. Einmahl, J.H.J. & de Haan, L.F.M. & Krajina, A., 2009. "Estimating Extreme Bivariate Quantile Regions," Discussion Paper 2009-29, Tilburg University, Center for Economic Research.
    82. 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.
    83. Susmel, Raul, 2001. "Extreme observations and diversification in Latin American emerging equity markets," Journal of International Money and Finance, Elsevier, vol. 20(7), pages 971-986, December.
    84. repec:ner:tilbur:urn:nbn:nl:ui:12-125712 is not listed on IDEAS
    85. Longin, Francois, 2005. "The choice of the distribution of asset returns: How extreme value theory can help?," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 1017-1035, April.
    86. Gencay, Ramazan & Selcuk, Faruk, 2006. "Overnight borrowing, interest rates and extreme value theory," European Economic Review, Elsevier, vol. 50(3), pages 547-563, April.
    87. Chen Zou, 2009. "Dependence structure of risk factors and diversification effects," DNB Working Papers 219, Netherlands Central Bank, Research Department.
    88. 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.
    89. 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.
    90. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-081, New York University, Leonard N. Stern School of Business-.
    91. Cotter, John & Dowd, Kevin, 2007. "The tail risks of FX return distributions: A comparison of the returns associated with limit orders and market orders," Finance Research Letters, Elsevier, vol. 4(3), pages 146-154, September.
    92. Cotter, John & Longin, Francois, 2004. "Margin setting with high-frequency data," MPRA Paper 3528, University Library of Munich, Germany, revised 2006.
    93. Sheri Markose & Amadeo Alentorn, 2005. "The Generalized Extreme Value (GEV) Distribution, Implied Tail Index and Option Pricing," Economics Discussion Papers 594, University of Essex, Department of Economics.
    94. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    95. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
    96. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
    97. Jon Danielsson, 2000. "The Emperor has no Clothes: Limits to Risk Modelling," FMG Special Papers sp126, Financial Markets Group.
    98. Pownall, Rachel A. J. & Koedijk, Kees G., 1999. "Capturing downside risk in financial markets: the case of the Asian Crisis," Journal of International Money and Finance, Elsevier, vol. 18(6), pages 853-870, December.
    99. John Cotter, 2006. "Extreme Value Estimation of Boom and Crash Statistics," The European Journal of Finance, Taylor & Francis Journals, vol. 12(6-7), pages 553-566.
    100. de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August.
    101. Wagner, Niklas, 2005. "Autoregressive conditional tail behavior and results on Government bond yield spreads," International Review of Financial Analysis, Elsevier, vol. 14(2), pages 247-261.
    102. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
    103. Gencay, Ramazan & Selcuk, Faruk, 2004. "Extreme value theory and Value-at-Risk: Relative performance in emerging markets," International Journal of Forecasting, Elsevier, vol. 20(2), pages 287-303.
    104. Olivier V. Pictet & Michel M. Dacorogna & Ulrich A. Muller, 1996. "Hill, Bootstrap and Jackknife Estimators for Heavy Tails," Working Papers 1996-12-10, Olsen and Associates.
    105. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    106. Starica, Catalin, 1999. "Multivariate extremes for models with constant conditional correlations," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 515-553, December.
    107. Benoit Mandelbrot, 1967. "The Variation of Some Other Speculative Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 393.
    108. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
    109. Namwon Hyung & Casper G. de Vries, 2005. "Portfolio Diversification Effects of Downside Risk," Tinbergen Institute Discussion Papers 05-008/2, Tinbergen Institute.
    110. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    111. V. Chavez-Demoulin & A. C. Davison & A. J. McNeil, 2005. "Estimating value-at-risk: a point process approach," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 227-234.
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