Filtered Extreme Value Theory for Value-At-Risk Estimation
AbstractExtreme 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 3302.
Date of creation: 22 May 2007
Date of revision:
Value at-Risk; Filtered Expected shortfall; Extreme value theory; emerging markets;
Find related papers by 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
- G0 - Financial Economics - - General
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-05-26 (All new papers)
- NEP-CFN-2007-05-26 (Corporate Finance)
- NEP-ECM-2007-05-26 (Econometrics)
- NEP-FOR-2007-05-26 (Forecasting)
- NEP-RMG-2007-05-26 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- Peter F. Christoffersen & Francis X. Diebold, 1998.
"How Relevant is Volatility Forecasting for Financial Risk Management?,"
NBER Working Papers
6844, National Bureau of Economic Research, Inc.
- Peter F. Christoffersen & Francis X. Diebold, 2000. "How Relevant is Volatility Forecasting for Financial Risk Management?," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 12-22, February.
- 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 98-080, New York University, Leonard N. Stern School of Business-.
- Peter F. Christoffersen & Francis X. Diebold, 1997. "How Relevant is Volatility Forecasting for Financial Risk Management?," Center for Financial Institutions Working Papers 97-45, Wharton School Center for Financial Institutions, University of Pennsylvania.
- 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.
- Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
- 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.
- 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.
- Turan G. Bali, 2003. "An Extreme Value Approach to Estimating Volatility and Value at Risk," The Journal of Business, University of Chicago Press, vol. 76(1), pages 83-108, January.
- 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.
- Assaf, A., 2006. "Dependence and mean reversion in stock prices: The case of the MENA region," Research in International Business and Finance, Elsevier, vol. 20(3), pages 286-304, September.
- Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
- 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, vol. 12(1), pages 1-22.
- 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.
- 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.
- 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.
- Juan-Angel Jimenez-Martin & Michael McAleer & Teodosio Perez Amaral & Paulo Araujo Santos, 2013.
"GFC-Robust Risk Management under the Basel Accord using Extreme Value Methodologies,"
Tinbergen Institute Discussion Papers
13-070/III, Tinbergen Institute.
- 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.
- Santos, P.A. & Jimenez-Martin, J-A. & McAleer, M.J. & Perez-Amaral, T., 2011. "GFC-Robust Risk Management Under the Basel Accord Using Extreme Value Methodologies," Econometric Institute Research Papers EI2011-27, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- 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 11/28, University of Canterbury, Department of Economics and Finance.
- 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," Documentos del Instituto Complutense de AnÃ¡lisis EconÃ³mico 2011-27, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
- Michael McAleer & Paulo Araújo Santos & Juan-Ángel Jiménez-Martín & Teodosio Pérez Amaral, 2011. "GFC-Robust Risk Management Under the Basel Accord Using Extreme Value Methodologies," KIER Working Papers 782, Kyoto University, Institute of Economic Research.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Ekkehart Schlicht).
If references are entirely missing, you can add them using this form.