Estimation of Value at Risk: extreme value and and robust approaches
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The large portfolios of traded assets held by many financial institutions have made the measurement of market risk a necessity. In practice, VaR measures are computed for several holding periods and confidence levels. A key issue in implementing VaR and related risk measures is to obtain accurate estimates for the tails of the conditional profit and loss distribution at the relevant horizons. VaR forecasts can be heavily affected by a few influential points, especially when long forecast horizons are considered. Robustness can be enhanced by fitting a generalized Pareto distribution to the tails of the distribution of the residual and sampling tail residuals from this density. However, to ensure a sufficiently large breakdown point for the estimator of the generalized Pareto tails, robust estimation is needed (see Dell’Aquila, Ronnchetti, 2006). The aim of the paper is to compare selected approaches to computing Value at Risk. We consider classical and robust conditional (GARCH) and unconditional (EVT) semi-nonparametric models where tail events are modeled using the generalized Pareto distribution. We wish to answer the question of whether the robust semi-nonparametric procedure generates more accurate VaRs than the classical approach does.
- Department of Demography and Business Statistics, Karol Adamiecki University of Economics, ul. Bogucicka 14, 40-226 Katowice, Poland, email@example.com
- Department of Demography and Business Statistics, Karol Adamiecki University of Economics, ul. Bogucicka 14, 40-226 Katowice, Poland, firstname.lastname@example.org
- BALI T.G., An extreme value approach to estimating volatility and value at risk, Journal of Business 2003, Vol. 76, No. 1, 83–108.
- BRAZAUSKAS V., SERFING R., Robust estimation of tail parameters for two-parameter and exponential models via generalized quantile statistics, Extremes, 2000, Vol. No. 3, 231–249.
- BROOKS C., CLARE A.D., DALE MOLLE J.W., PERSAND G., A comparison of extreme value theory approaches for determining value at risk, Journal of Empirical Finance, 2005, Vol. 12, 339–352.
- DELL’AQUILA R., EMBRECHTS P., Extremes and robustness: a contradiction? Springer, Berlin–Heidelberg– New York, 2006.
- EFRON B., The jackknife, the bootstrap and other resampling plans, Society of Industrial and Applied Mathematics CBMS-NSF Monographs, 1982, Vol. 38.
- HAMPEL F., RONCHETTI E., ROUSSEEUW P., STAHEL W., Robust Statistics: The Approach Based on Influence Functions, Wiley, New York, 1986.
- HUBER P., Robust estimation of a location parameter, Annals of Mathematical Statistics, 1964, Vol. 35, No. 1, 73–101.
- HUBER P.J., Robust Statistics, Wiley, New York, 1981.
- HSIEH D.A., Implications of nonlinear dynamics for financial risk management, Journal of Financial and Quantitative Analysis, 1993, Vol. 28, No. 1, 41–64.
- JOHNSON N.L., Systems of frequency curves generated by methods of translations, Biometrika, 1949, Vol. 36, 149–176.
- JUÁREZ S., SCHUCANY W., Robust and efficient estimation for the generalized Pareto distribution, Extremes, 2004, Vol. 7, No. 32, 231–257.
- KENDALL M.G., STUART A., ORD J.K., Kendall’s Advanced Theory of Statistics, Oxford University Press, New York, 1987.
- MANCINI L., TROJANI F., Robust Value at Risk Prediction, Swiss Finance Institute Research Paper Series, 2007, No. 31, pp.
- MCNEIL A.J., FREY R., Estimation of tail-related risk measures for heteroscedastic financial time series: An extreme value approach, Journal of Empirical Finance, 2000, Vol. 7, 271–300.
- NEFTCI S.N., Value at Risk Calculations, Extreme Events, and Tail Estimation, The Journal of Derivatives, 2000, Vol. 7, 23–37.
- PENG L., WELSH A., Robust estimation of the generalized Pareto distribution, Extremes, 2001, Vol. 4, No. 1, 53–65.
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