Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation

Ghorbel, Ahmed and Trabelsi, Abdelwahed (2007): Predictive Performance of Conditional Extreme Value Theory and Conventional Methods in Value at Risk Estimation.

Abstract

This paper conducts a comparative evaluation of the predictive performance of various Value at Risk (VaR) models such as GARCH-normal, GARCH-t, EGARCH, TGARCH models, variance-covariance method, historical simulation and filtred Historical Simulation, EVT and conditional EVT methods. Special emphasis is paid on two methodologies related to the Extreme Value Theory (EVT): The Peaks over Threshold (POT) and the Block Maxima (BM). Both estimation techniques are based on limits results for the excess distribution over high thresholds and block maxima, respectively. We apply both unconditional and conditional EVT models to management of extreme market risks in stock markets. They are applied on daily returns of the Tunisian stock exchange (BVMT) and CAC 40 indexes with the intension to compare the performance of various estimation methods on markets with different capitalization and trading practices. The sample extends over the period July 29, 1994 to December 30, 2005. We use a rolling windows of approximately four years (n= 1000 days). The sub-period from July, 1998 for BVMT (from August 4, 1998 for CAC 40) has been reserved for backtesting purposes. The results we report demonstrate that conditional POT-EVT method produces the most accurate forecasts of extreme losses both for standard and more extreme VaR quantiles. The conditional block maxima EVT method is less accurate.

• Item Type: MPRA Paper
• Institution: Institut Supérieur de Gestion, Laboratoire BESTMOD, Université de Tunis
• Language: English
• Keywords: Financial Risk management; Value-at-Risk; Extreme Value Theory; Conditional EVT; Backtesting
• Subjects: G - Financial Economics > G0 - General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; G - Financial Economics > G1 - General Financial Markets > G15 - International Financial Markets

References

Andersen, T.G. and T. Bollerslev (1998), Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts International Economic Review 39, 885-905. Andersen, T.G., T. Bollerslev, P.F. Christoffersen and F.X. Diebold (2005), Practical Volatility and Correlation Modeling for Financial Market Risk Management in M. Carey and R. Stulz 29 (eds.), Risks of Financial Institutions. Chicago: University of Chicago Press for National Bureau of Economic Research. Andersen, T.G., T. Bollerslev and F.X. Diebold (2003), Some Like It Smooth and Some Like It Rough: Untangling Continuous and Jump Components in Measuring, Modeling and Forecasting Asset Return Volatility, Working paper, Northwestern University, Duke University and University of Pennsylvania. Andersen, T., T. Bollerslev, F.X. Diebold, and P. Labys (1999), (Understanding, Optimizing, Using and Forecasting) Realized Volatility and Correlation, Working Paper, Northwestern University, Duke University and University of Pennsylvania. Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.(1999), Coherent measures of risk. Mathematical Finance 9, 203 228. Artzner, P., Delbaen, F., Eber, J.-M., Heath, D.(2000), Risk management and capital allocation with coherent measures of risk, October. Available from <www.math.ethz.ch/finance> Bystrom Hans (2004), Managing extreme risks in tranquil and volatile markets using conditional extreme value theory. International Review of Financial Analysis 13 (2004) 133 152. Bekiros Stelios D, Dimitris A. Georgoutsos (2005), Estimation of Value-at-Risk by extreme value and conventional methods: a comparative evaluation of their predictive performance. Int. Fin. Markets, Inst. and Money 15 (2005) 209 228 Berkowitz, J. O Brien, (2002) How accurate are value-at-risk models at commercial banks?, Journal of Finance 57 -1093 1111. Chris Brooks and Gita Persand, (2003), Volatility forecasting for risk management, Journal of Forecasting, 22, 1-22. Christoffersen, P., Diebold, F.X. (2000), How relevant is volatility forecasting for financial risk management?, Review of Economics and Statistics 82, 12 22. Diebold F.X., T. Schuermann and J.D. Stroughair (1998), Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management, in P. Refenes (ed.), Computational Finance, Kluwer Acadmic Press, Boston. Engle, R. (2001). GARCH 101: The use of ARCH/GARCH models in applied econometrics. Journal of Economic Perspectives, 15(4), 157 168. Gençay, Selçuk, Ulugulyagci (2003), High volatility, thick tails and extreme value theory, Insurance: Mathematics and Economics.33 337 356. Hansen, P.R. and A. Lunde (2005), A Forecast Comparison of Volatility Models: Does Anything Beat a GARCH(1,1)? Journal of Applied Econometrics, forthcoming. Kupiec, (1995) Techniques for verifying the accuracy of risk measurement models, Journal of Derivatives 2 ,73 84. Longin F.M. (2000), From value at risk to stress testing: The extreme value approach, Journal of Banking and Finance, 24, 1097 1130. Manganelli, S., Engle, R.F.(2001) Value at risk models in finance, WP N_ 75, ECB, Frankfurt, August. Available from <http://www.gloriamundi.org/var/pub/maneng.pdf> McNeil, A., & Frey, R.(2000). Estimation of tail-related risk measures for heteroscedastic financial times series: An extreme value approach. Journal of Empirical Finance 7, 271 300. Poon S.-H. and C. Granger (2003), Forecasting volatility in financial markets: a review, Journal of Economic Literature, XLI, 478-539. Viviana Fernandez (2005), Risk management under extreme events. International Review of Financial Analysis 14 113 148 Szego G. ( 2002), Measures of risk. Journal of Banking & Finance 26 1253 1272 Zivot, E., & Wang, J. (2003). Modeling financial times series with S-Plus. Seattle, WA 98109- 3044: Insightful Corporation (Global Headquarters).