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Robust Value at Risk Prediction


  • Loriano Mancini


  • Fabio Trojani



We propose a general robust semiparametric bootstrap method to estimate conditional predictive distributions of GARCH-type models. Our approach is based on a robust estimator for the parameters in GARCH-type models and a robustified resampling method for standardized GARCH residuals, which controls the bootstrap instability due to influential observations in the tails of standardized GARCH residuals. Monte Carlo simulation showsthat our method consistently provides lower VaR forecast errors, often to a large extent, and in contrast to classical methods never fails validation tests at usual significance levels. We test extensively our approach in the context of real data applications to VaR prediction for market risk, and find that only our robust procedure passes all validation tests at usualconfidence levels. Moreover, the smaller tail estimation risk of robust VaR forecasts implies VaR prediction intervals that can be nearly 20% narrower and 50% less volatile over time. This is a further desirable property of our method, which allows to adapt risky positions to VaR limits more smoothly and thus more efficiently.

Suggested Citation

  • Loriano Mancini & Fabio Trojani, 2007. "Robust Value at Risk Prediction," University of St. Gallen Department of Economics working paper series 2007 2007-36, Department of Economics, University of St. Gallen.
  • Handle: RePEc:usg:dp2007:2007-36

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    References listed on IDEAS

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    Cited by:

    1. Hotta, Luiz & Trucíos, Carlos & Ruiz, Esther, 2015. "Robust bootstrap forecast densities for GARCH models: returns, volatilities and value-at-risk," DES - Working Papers. Statistics and Econometrics. WS ws1523, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Francq, Christian & Zakoian, Jean-Michel, 2015. "Joint inference on market and estimation risks in dynamic portfolios," MPRA Paper 68100, University Library of Munich, Germany.
    3. 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.
    4. esposito, francesco paolo & cummins, mark, 2015. "Multiple hypothesis testing of market risk forecasting models," MPRA Paper 64986, University Library of Munich, Germany.
    5. Dias, Alexandra, 2013. "Market capitalization and Value-at-Risk," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5248-5260.
    6. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    7. Kellner, Ralf & Rösch, Daniel, 2016. "Quantifying market risk with Value-at-Risk or Expected Shortfall? – Consequences for capital requirements and model risk," Journal of Economic Dynamics and Control, Elsevier, vol. 68(C), pages 45-63.

    More about this item


    Backtesting; M-estimator; Extreme Value Theory; Breakdown Point;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C59 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Other

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