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A Comparison Of Some Univariate Models For Value-At-Risk And Expected Shortfall

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  • CARLO MARINELLI

    (Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany)

  • STEFANO D'ADDONA

    (Department of International Studies, University of Rome III, Via G. Chiabrera 199, 00145 Rome, Italy)

  • SVETLOZAR T. RACHEV

    (School of Economics and Business Engineering, University of Karlsruhe, Kollegium am Schloss, Bau II, 20.12, R210 D-76128 Karlsruhe, Germany;
    Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA)

Abstract

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

Suggested Citation

  • Carlo Marinelli & Stefano D'Addona & Svetlozar T. Rachev, 2007. "A Comparison Of Some Univariate Models For Value-At-Risk And Expected Shortfall," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(06), pages 1043-1075.
    • Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:06:n:s0219024907004548
    DOI: 10.1142/S0219024907004548
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    References listed on IDEAS

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    1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 2000. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Journal of Risk Finance, Emerald Group Publishing Limited, vol. 1(2), pages 30-35, January.
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    Cited by:

    1. Szubzda Filip & Chlebus Marcin, 2019. "Comparison of Block Maxima and Peaks Over Threshold Value-at-Risk models for market risk in various economic conditions," Central European Economic Journal, Sciendo, vol. 6(53), pages 70-85, January.
    2. Bayer, Sebastian, 2018. "Combining Value-at-Risk forecasts using penalized quantile regressions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 56-77.
    3. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2017. "Risk quantification in turmoil markets," Risk Management, Palgrave Macmillan, vol. 19(3), pages 202-224, August.
    4. Fernanda Maria Müller & Marcelo Brutti Righi, 2024. "Comparison of Value at Risk (VaR) Multivariate Forecast Models," Computational Economics, Springer;Society for Computational Economics, vol. 63(1), pages 75-110, January.
    5. Fernanda Maria Müller & Marcelo Brutti Righi, 2018. "Numerical comparison of multivariate models to forecasting risk measures," Risk Management, Palgrave Macmillan, vol. 20(1), pages 29-50, February.
    6. Antonio Díaz & Gonzalo García-Donato & Andrés Mora-Valencia, 2019. "Quantifying Risk in Traditional Energy and Sustainable Investments," Sustainability, MDPI, vol. 11(3), pages 1-22, January.

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