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Filtered Extreme Value Theory for Value-At-Risk Estimation

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  • Ozun, Alper
  • Cifter, Atilla
  • Yilmazer, Sait

Abstract

Extreme returns in stock returns need to be captured for a successful risk management function to estimate unexpected loss in portfolio. Traditional value-at-risk models based on parametric models are not able to capture the extremes in emerging markets where high volatility and nonlinear behaviors in returns are observed. The Extreme Value Theory (EVT) with conditional quantile proposed by McNeil and Frey (2000) is based on the central limit theorem applied to the extremes rater than mean of the return distribution. It limits the distribution of extreme returns always has the same form without relying on the distribution of the parent variable. This paper uses 8 filtered EVT models created with conditional quantile to estimate value-at-risk for the Istanbul Stock Exchange (ISE). The performances of the filtered expected shortfall models are compared to those of GARCH, GARCH with student-t distribution, GARCH with skewed student-t distribution and FIGARCH by using alternative back-testing algorithms, namely, Kupiec test (1995), Christoffersen test (1998), Lopez test (1999), RMSE (70 days) h-step ahead forecasting RMSE (70 days), number of exception and h-step ahead number of exception. The test results show that the filtered expected shortfall has better performance on capturing fat-tails in the stock returns than parametric value-at-risk models do. Besides increase in conditional quantile decreases h-step ahead number of exceptions and this shows that filtered expected shortfall with higher conditional quantile such as 40 days should be used for forward looking forecasting.

Suggested Citation

  • Ozun, Alper & Cifter, Atilla & Yilmazer, Sait, 2007. "Filtered Extreme Value Theory for Value-At-Risk Estimation," MPRA Paper 3302, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:3302
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    File URL: https://mpra.ub.uni-muenchen.de/3302/1/MPRA_paper_3302.pdf
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    References listed on IDEAS

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    6. 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.
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    Citations

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    Cited by:

    1. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, Open Access Journal, vol. 2(2), pages 1-15, May.
    2. Jimenez-Martin, Juan-Angel & McAleer, Michael & Pérez-Amaral, Teodosio & Santos, Paulo Araújo, 2013. "GFC-robust risk management under the Basel Accord using extreme value methodologies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 223-237.
    3. Sasa Zikovic & Bora Aktan, 2009. "Global financial crisis and VaR performance in emerging markets: A case of EU candidate states - Turkey and Croatia," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics, vol. 27(1), pages 149-170.
    4. Stavros Degiannakis & Christos Floros & Alexandra Livada, 2012. "Evaluating value-at-risk models before and after the financial crisis of 2008: International evidence," Managerial Finance, Emerald Group Publishing, vol. 38(3), pages 436-452, March.
    5. Amira Akl Ahmed & Doaa Akl Ahmed, 2016. "Modelling Conditional Volatility and Downside Risk for Istanbul Stock Exchange," Working Papers 1028, Economic Research Forum, revised Jul 2016.
    6. Stavros Degiannakis & Christos Floros & Alexandra Livada, 2012. "Evaluating value-at-risk models before and after the financial crisis of 2008: International evidence," Managerial Finance, Emerald Group Publishing, vol. 38(4), pages 436-452, March.
    7. Marcin Chlebus, 2016. "EWS-GARCH: New Regime Switching Approach to Forecast Value-at-Risk," Working Papers 2016-06, Faculty of Economic Sciences, University of Warsaw.

    More about this item

    Keywords

    Value at-Risk; Filtered Expected shortfall; Extreme value theory; emerging markets;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G0 - Financial Economics - - General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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