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Which Extreme Values Are Really Extreme?

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  • Jesus Gonzalo

Abstract

We define the extreme values of any random sample of size n from a distribution function F as the observations exceeding a threshold and following a type of generalized Pareto distribution (GPD) involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD. To formalize the definition we use a semiparametric bootstrap to test the corresponding GPD approximation. Finally, we use our methodology to estimate the tail index and value at risk (VaR) of some financial indexes of major stock markets. Copyright 2004, Oxford University Press.

Suggested Citation

  • Jesus Gonzalo, 2004. "Which Extreme Values Are Really Extreme?," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 349-369.
    • Handle: RePEc:oup:jfinec:v:2:y:2004:i:3:p:349-369
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    File URL: http://hdl.handle.net/10.1093/jjfinec/nbh014
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    Cited by:

    1. Schluter, Christian & Trede, Mark, 2008. "Identifying multiple outliers in heavy-tailed distributions with an application to market crashes," Journal of Empirical Finance, Elsevier, vol. 15(4), pages 700-713, September.
    2. Ana-Maria Gavril, 2009. "Exchange Rate Risk: Heads or Tails," Advances in Economic and Financial Research - DOFIN Working Paper Series 35, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    3. Charles, Amélie & Darné, Olivier, 2014. "Large shocks in the volatility of the Dow Jones Industrial Average index: 1928–2013," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 188-199.
    4. Loriano Mancini & Fabio Trojani, 2011. "Robust Value at Risk Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 281-313, Spring.
    5. Juncal Cunado Eizaguirre & Javier Gomez Biscarri & Fernando Perez de Gracia Hidalgo, 2009. "Financial liberalization, stock market volatility and outliers in emerging economies," Applied Financial Economics, Taylor & Francis Journals, vol. 19(10), pages 809-823.
    6. Francine Gresnigt & Erik Kole & Philip Hans Franses, 2017. "Exploiting Spillovers to Forecast Crashes," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 36(8), pages 936-955, December.
    7. Alfonso Novales & Laura Garcia-Jorcano, 2019. "Backtesting Extreme Value Theory models of expected shortfall," Documentos de Trabajo del ICAE 2019-24, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    8. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    9. Koopman, Siem Jan & Shephard, Neil & Creal, Drew, 2009. "Testing the assumptions behind importance sampling," Journal of Econometrics, Elsevier, vol. 149(1), pages 2-11, April.
    10. Nikola Radivojevic & Milena Cvjetkovic & Saša Stepanov, 2016. "The new hybrid value at risk approach based on the extreme value theory," Estudios de Economia, University of Chile, Department of Economics, vol. 43(1 Year 20), pages 29-52, June.
    11. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2013. "Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2325-2352, May.
    12. 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.
    13. Olmo, J., 2009. "Extreme Value Theory Filtering Techniques for Outlier Detection," Working Papers 09/09, Department of Economics, City University London.
    14. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    15. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    16. 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.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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