Ozun, Alper and Cifter, Atilla and Yilmazer, Sait (2007): Filtered Extreme Value Theory for Value-At-Risk Estimation.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Filtered Extreme Value Theory for Value-At-Risk Estimation|
|Keywords:||Value at-Risk; Filtered Expected shortfall; Extreme value theory; emerging markets|
|Subjects:||C - Mathematical and Quantitative Methods > C3 - Multiple or Simultaneous Equation Models; Multiple Variables > C32 - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
G - Financial Economics > G0 - General
C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C52 - Model Evaluation, Validation, and Selection
|Depositing User:||Atilla Cifter|
|Date Deposited:||22. May 2007|
|Last Modified:||13. Feb 2013 00:18|
Acerbi, C. (2002). Spectral Measures of Risk: A Coherent Representation of Subjective Risk Aversion. Journal of Banking and Finance, 26(7), 1505-1518. Altay, S. & Kucukozmen, C. (2006). An Assessment of Value-at-Risk (VaR) and Expected Tail Loss (ETL) Under a Stress Testing Framework for Turkish Stock Market, Proceedings of ICBME, Yasar University, Izmir. Amin, G. & Kat, H. (2003). Hedge Fund Performance 1990-2000: Do the Money Machines Really Add Value?. Journal of Financial and Quantitative Analysis, 38, 1-24. Artzner, P., F., Delbaen, J., Eber, M. & Heath, D. (1999). Coherent Measures of Risk. Mathematical Finance, 9, 203–228. Assaf, A. (2006). Dependence and Mean Reversion in Stock Prices: The Case of the MENA region. Research in International Business and Finance, 20(3), 286-304. Christoffersen, P. (1998). Evaluating Interval Forecasts. International Economic Review, (39), 841-862. Christoffersen, P. & Diebold, F.X. (2000). How relevant is volatility forecasting for financial risk management?. Review of Economics and Statistics 82, 12-22. Cifter, A., Ozun, A. & Yilmazer, S. (2007). Value-at-Risk with Expected Short Fall and Generalized Pareto Distribution: Some Comparative Evidence For Turkish Interest Rate Markets, TBB Bankacılar Dergisi (Banks Association of Turkey-Bankers’ Journal), 60, 3-16 (in Turkish). Bali, T. (2003). An Extreme Value Approach to Estimating Volatility and Value at Risk. Journal of Business, 76(1), 83-108. Blum, P., Dias, A. & Embrechts, P. (2002). The Art of Dependence Modeling: The Latest Advances in Correlation Analysis. In: M. Lane (Eds.): Alternative Risk Strategies, Risk Books, London. Dickey, D.A. & Fuller, W.A. (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica, 49, 1057–1072. Diebold, F. & Mariano, R.S. (1995). Comparing Predictive Accuracy. Journal of Business & Economics Statistics, 13(3), 253-263 Dowd, K. (2004). FOMC Forecasts of Macroeconomic Risks, Occasional Papers 12, Industrial Economics Division. Gilli, K. & Kellezi, E. (2002). Portfolio Optimization with VaR and Expected Shortfall. In: E.J. Kontoghiorghes et al. (Eds.), Computational Methods in Decision-making, Economics and Finance, Kluwer Applied Optimization Series, 167-183. Chung, C.F. (1999). Estimating the Fractionally Integrated GARCH Model. National Taiwan University, Working Paper. Baillie, R.T., Bollerslev, T. & Mikkelsen, H. (1996). Fractionally Integrated Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 74, 3-30. Davidson, J. (2002). Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, Working Paper, http://www.cf.ac.uk/carbs/econ/davidsonje/. Accessed on 10 April 2007. Embrechts P., Kluppelberg, C. & Mikosch, T. (1997). Modeling Extremal Events For Insurance and finance, Berlin: Springer Press. Eksi, Z., Yildirim, I. & Yildirak, K. (2006). Alternative Risk Measures and Extreme Value Theory In Finance: Implementation on ISE 100 Index. Proceedings of ICBME, Yasar University, Izmir. Focardı, S. & Fabozzı, F. (2003). Fat Tails, Scaling and Stable Laws. Journal of Risk Finance, 5(1), 25-36. Focardı, S. & Fabozzı, F. (2004). The Mathematics of Financial Modeling and Investment Management, New York: John Wiley & Sons. Gencay, R. & Selcuk, F. (2004). Extreme Value Theory and Value-at-Risk: Relative Perfomance in Emerging Markets. International Journal of Forecasting, 20, 287-303. Gencay, R., Selcuk, F. & Ulugulyagci, A. (2003). High Volatility, Thick Tails and Extreme Value Theory in Value-at-Risk Estimation. Insurance, Mathematics and Economics, 33, 337-356. Gupta, A. & Liang, B. (2005). Do Hedge Funds Have Enough Capital? A Value-at-Risk Approach. Journal of Financial Economics, 77, 35-47. Inui, K. & Kijima, M. (2005). On the Significance of Expected Shortfall as a Coherent Risk Measure. Journal of Banking and Finance, 29, 853–864. Mcneil, A. J. & Frey, R. (2000). Estimation of Tail-related Risk Measures for Heteroscedastic Financial Time Series: An extreme value approach. Journal of Empirical Finance, 7, 271-300. Neftci, S. (2000). Value at Risk Calculations, Extreme Events, and Tail Estimation. The Journal of Derivatives, Spring, 12-19. Kupiec, P.H. (1995). Techniques for Verifying the Accuracy of Risk Measurement Models. Journal of Derivatives, Winter, 73-84 Lopez, J.A. (1999). Methods for Evaluating Value-at-Risk Models. Federal Reserve Bank of San Francisco Economic Review, 2, 3-17. Longin, F. M. (2000). From Value At Risk To Stress Testing: The Extreme Value Approach. Journal of Banking and Finance, 24, 1097-1130. Kuester, K., Mittik, S. &.Paolella, M.S. (2005). Value-at-risk Prediction: A Comparison of Alternative Strategies. Journal of Financial Econometrics 4(1), 53-89. Kalyvas, L., Steftos, A., Sriopoulos, C. & Georgopoulos, A. (2007). An Investigation of Riskiness in South and Eastern European Markets. International Journal of Financial Services Management 2(1-2). 13-21. Liang, B. & Park, H. (2007). Risk Measures For Hedge Funds: A Cross-Sectional Approach. European Financial Management, 13(2), 333-370 Lhabitant, F.S. (2002). Hedge Funds: Myths and Limits, New York: John Wiley & Sons. Laurent, S. & Peters, J.P. (2002). G@rch 2.30: An Ox Package for Estimating and Forecasting Various ARCH Models. Université de Liège, Working Paper Martinz, F.C. & Yao, F. (2006). Estimation of Value-At-Risk And Expected Shortfall Based on Nonlinear Models of Return Dynamics And Extreme Value Theory. Studies in Nonlinear Dynamics and Econometrics, 10(2), 107-149. Philips, P.C.B. & Perron, P. (1988). Testing for a Unit Root in Time Series Regression. Biometrica, 75, 335-446 Poon, S., Rockınger, M. & Tawn, J. (2004). Extreme Value Dependence in Financial Markets: Diagnostics, Models and Financial Implications. The Review of Financial Studies, 17(2), 586-610 Saltoglu, B. (2003). A High Frequency Analysis of Financial Risk and Crisis: An Empirical Study on Turkish Financial Market, Istanbul: Yaylim Press. Tolikas K. & Brown, R. (2006). The Distribution of The Extreme Daily Share Returns in The Athens Stock Exchange. The European Journal of Finance, 12(1), 1-22. Yamai, Y. & Yoshiba, T. (2005). Value-at-risk Versus Expected Shortfall: A Practical Perspective. Journal of Banking and Finance, 29(4), 997-1015.