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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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 3302.

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Date of creation: 22 May 2007
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Handle: RePEc:pra:mprapa:3302

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

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References

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  1. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  2. Turan G. Bali, 2003. "An Extreme Value Approach to Estimating Volatility and Value at Risk," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 76(1), pages 83-108, January.
  3. Gupta, Anurag & Liang, Bing, 2005. "Do hedge funds have enough capital? A value-at-risk approach," Journal of Financial Economics, Elsevier, Elsevier, vol. 77(1), pages 219-253, July.
  4. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1505-1518, July.
  5. Peter F. Christoffersen & Francis X. Diebold, 1998. "How Relevant is Volatility Forecasting for Financial Risk Management?," New York University, Leonard N. Stern School Finance Department Working Paper Seires, New York University, Leonard N. Stern School of Business- 98-080, New York University, Leonard N. Stern School of Business-.
  6. Assaf, A., 2006. "Dependence and mean reversion in stock prices: The case of the MENA region," Research in International Business and Finance, Elsevier, Elsevier, vol. 20(3), pages 286-304, September.
  7. 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, Elsevier, vol. 7(3-4), pages 271-300, November.
  8. 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.
  9. Konstantinos Tolikas & Richard Brown, 2006. "The distribution of the extreme daily share returns in the Athens stock exchange," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 12(1), pages 1-22.
  10. Yamai, Yasuhiro & Yoshiba, Toshinao, 2005. "Value-at-risk versus expected shortfall: A practical perspective," Journal of Banking & Finance, Elsevier, Elsevier, vol. 29(4), pages 997-1015, April.
  11. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, Econometric Society, vol. 49(4), pages 1057-72, June.
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  13. 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.
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Cited by:
  1. 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, Emerald Group Publishing, vol. 38(3), pages 436-452, March.
  2. 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.
  3. Paulo Araújo Santos & Juan-Ángel Jiménez-Martín & Michael McAleer & Teodosio Pérez Amaral, 2011. "GFC-Robust Risk Management Under the Basel Accord Using Extreme Value Methodologies," Working Papers in Economics, University of Canterbury, Department of Economics and Finance 11/28, University of Canterbury, Department of Economics and Finance.
  4. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, Open Access Journal, MDPI, Open Access Journal, vol. 2(2), pages 211-225, May.

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