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Comparison of Methods for Estimating the Uncertainty of Value at Risk

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  • Santiago Gamba Santamaría
  • Oscar Fernando Jaulín Méndez
  • Luis Fernando Melo Velandia
  • Carlos Andrés Quicazán Moreno

Abstract

Value at Risk (VaR) is a market risk measure widely used by risk managers and market regulatory authorities. There is a variety of methodologies proposed in the literature for the estimation of VaR. However, few of them get to say something about its distribution or its confidence intervals. This paper compares different methodologies for computing such intervals. Several methods, based on asymptotic normality, extreme value theory and subsample bootstrap, are used. Using Monte Carlo simulations, it is found that these approaches are only valid for high quantiles. In particular, there is a good performance for VaR (99%), in terms of coverage rates, and bad performance for VaR (95%) and VaR (90%). The results are confirmed by an empirical application for the stock market index returns of G7 countries.

Suggested Citation

  • Santiago Gamba Santamaría & Oscar Fernando Jaulín Méndez & Luis Fernando Melo Velandia & Carlos Andrés Quicazán Moreno, 2016. "Comparison of Methods for Estimating the Uncertainty of Value at Risk," Borradores de Economia 14263, Banco de la Republica.
    • Handle: RePEc:col:000094:014263
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    References listed on IDEAS

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    1. Moraux, Franck, 2011. "How valuable is your VaR? Large sample confidence intervals for normal VaR," Journal of Risk Management in Financial Institutions, Henry Stewart Publications, vol. 4(2), pages 189-200, March.
    2. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    3. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
    4. Gao, Feng & Song, Fengming, 2008. "ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1404-1424, October.
    5. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
    6. Peter Hall & Qiwei Yao, 2003. "Data tilting for time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 425-442, May.
    7. Leccadito, Arturo & Boffelli, Simona & Urga, Giovanni, 2014. "Evaluating the accuracy of value-at-risk forecasts: New multilevel tests," International Journal of Forecasting, Elsevier, vol. 30(2), pages 206-216.
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    Cited by:

    1. Nieto, María Rosa & Carmona-Benítez, Rafael Bernardo, 2018. "ARIMA + GARCH + Bootstrap forecasting method applied to the airline industry," Journal of Air Transport Management, Elsevier, vol. 71(C), pages 1-8.

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    More about this item

    Keywords

    Value at Risk; confidence intervals; data tilting; subsample bootstrap.;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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