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A detailed comparison of value at risk estimates

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  • Abad, Pilar
  • Benito, Sonia

Abstract

This work investigates the performance of different models of value at risk. We include several methods (parametric, historical simulation, Monte Carlo, and extreme value theory) and some models to compute the conditional variance. We analyze several international stock indexes and examine two types of periods: stable and volatile periods. To choose the best model, we employ a two-stage selection approach. The result indicates that the best model is a parametric model with conditional variance estimated by an asymmetric GARCH model under Student's t-distribution of returns. This paper shows that parametric models can obtain successful VaR measures if conditional variance is estimated properly.

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  • Abad, Pilar & Benito, Sonia, 2013. "A detailed comparison of value at risk estimates," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 94(C), pages 258-276.
    • Handle: RePEc:eee:matcom:v:94:y:2013:i:c:p:258-276
    DOI: 10.1016/j.matcom.2012.05.011
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    1. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    2. Panayiotis Theodossiou, 1998. "Financial Data and the Skewed Generalized T Distribution," Management Science, INFORMS, vol. 44(12-Part-1), pages 1650-1661, December.
    3. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    4. 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.
    5. Loriano Mancini & Fabio Trojani, 2011. "Robust Value at Risk Prediction," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 281-313, Spring.
    6. Jose A. Lopez, 1999. "Methods for evaluating value-at-risk estimates," Economic Review, Federal Reserve Bank of San Francisco, pages 3-17.
    7. Danielsson, Jon, 2002. "The emperor has no clothes: Limits to risk modelling," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1273-1296, July.
    8. 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 and Business, vol. 27(1), pages 149-170.
    9. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    10. Gonzalez-Rivera, Gloria & Lee, Tae-Hwy & Mishra, Santosh, 2004. "Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood," International Journal of Forecasting, Elsevier, vol. 20(4), pages 629-645.
    11. McDonald, James B. & Xu, Yexiao J., 1995. "A generalization of the beta distribution with applications," Journal of Econometrics, Elsevier, vol. 69(2), pages 427-428, October.
    12. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    14. Trino-Manuel Ñíguez, 2008. "Volatility and VaR forecasting in the Madrid Stock Exchange," Spanish Economic Review, Springer;Spanish Economic Association, vol. 10(3), pages 169-196, September.
    15. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
    16. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
    17. Ergün, A. Tolga & Jun, Jongbyung, 2010. "Time-varying higher-order conditional moments and forecasting intraday VaR and Expected Shortfall," The Quarterly Review of Economics and Finance, Elsevier, vol. 50(3), pages 264-272, August.
    18. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    19. Caporin, M. & McAleer, M.J., 2010. "Model Selection and Testing of Conditional and Stochastic Volatility Models," Econometric Institute Research Papers EI 2010-57, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    20. Consigli, Giorgio, 2002. "Tail estimation and mean-VaR portfolio selection in markets subject to financial instability," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1355-1382, July.
    21. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    22. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    23. Philip Yu & Wai Keung Li & Shusong Jin, 2010. "On Some Models for Value-At-Risk," Econometric Reviews, Taylor & Francis Journals, vol. 29(5-6), pages 622-641.
    24. Bali, Turan G. & Mo, Hengyong & Tang, Yi, 2008. "The role of autoregressive conditional skewness and kurtosis in the estimation of conditional VaR," Journal of Banking & Finance, Elsevier, vol. 32(2), pages 269-282, February.
    25. 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.
    26. repec:adr:anecst:y:2000:i:60:p:10 is not listed on IDEAS
    27. Jon Danielsson & Casper G. De Vries, 2000. "Value-at-Risk and Extreme Returns," Annals of Economics and Statistics, GENES, issue 60, pages 239-270.
    28. Susan Thomas & Mandira Sarma & Ajay Shah, 2003. "Selection of Value-at-Risk models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 22(4), pages 337-358.
    29. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    30. Giannopoulos, Kostas & Tunaru, Radu, 2005. "Coherent risk measures under filtered historical simulation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 979-996, April.
    31. Arnold Polanski & Evarist Stoja, 2010. "Incorporating higher moments into value-at-risk forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 29(6), pages 523-535.
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    Cited by:

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    2. Sonia Benito & Carmen López-Martín & Mª Ángeles Navarro, 2023. "Assessing the importance of the choice threshold in quantifying market risk under the POT approach (EVT)," Risk Management, Palgrave Macmillan, vol. 25(1), pages 1-31, March.
    3. Bayer, Sebastian, 2018. "Combining Value-at-Risk forecasts using penalized quantile regressions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 56-77.
    4. Chia-Lin Chang & David E. Allen & Michael McAleer & Ju-Ting Tang & Teodosio Pérez Amaral, 2013. "Risk Modelling and Management: An Overview," Documentos de Trabajo del ICAE 2013-22, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    5. Marcin Chlebus, 2016. "Can Lognormal, Weibull or Gamma Distributions Improve the EWS-GARCH Value-at-Risk Forecasts?," FindEcon Chapters: Forecasting Financial Markets and Economic Decision-Making, in: Magdalena Osińska (ed.), Statistical Review, vol. 63, 2016, 3, edition 1, volume 63, chapter 4, pages 329-350, University of Lodz.
    6. Xiaochun Liu, 2017. "An integrated macro‐financial risk‐based approach to the stressed capital requirement," Review of Financial Economics, John Wiley & Sons, vol. 34(1), pages 86-98, September.
    7. Mateusz Buczyński & Marcin Chlebus, 2021. "GARCHNet - Value-at-Risk forecasting with novel approach to GARCH models based on neural networks," Working Papers 2021-08, Faculty of Economic Sciences, University of Warsaw.
    8. Aleksander Schiffers & Marcin Chlebus, 2021. "The effectiveness of Value-at-Risk models in various volatility regimes," Working Papers 2021-28, Faculty of Economic Sciences, University of Warsaw.

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