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Comparison of methods for estimating the uncertainty of value at risk

Author

Listed:
  • Santiago Gamba-Santamaria
  • Oscar Fernando Jaulin-Mendez
  • Luis Fernando Melo-Velandia
  • Carlos Andrés Quicazán-Moreno

Abstract

Purpose - Value at risk (VaR) is a market risk measure widely used by risk managers and market regulatory authorities, and various methods are proposed in the literature for its estimation. However, limited studies discuss its distribution or its confidence intervals. The purpose of this paper is to compare different techniques for computing such intervals to identify the scenarios under which such confidence interval techniques perform properly. Design/methodology/approach - The methods that are included in the comparison are based on asymptotic normality, extreme value theory and subsample bootstrap. The evaluation is done by computing the coverage rates for each method through Monte Carlo simulations under certain scenarios. The scenarios consider different persistence degrees in mean and variance, sample sizes, VaR probability levels, confidence levels of the intervals and distributions of the standardized errors. Additionally, an empirical application for the stock market index returns of G7 countries is presented. Findings - The simulation exercises show that the methods that were considered in the study are only valid for high quantiles. In particular, in terms of coverage rates, there is a good performance for VaR(99 per cent) and bad performance for VaR(95 per cent) and VaR(90 per cent). The results are confirmed by an empirical application for the stock market index returns of G7 countries. Practical implications - The findings of the study suggest that the methods that were considered to estimate VaR confidence interval are appropriated when considering high quantiles such as VaR(99 per cent). However, using these methods for smaller quantiles, such as VaR(95 per cent) and VaR(90 per cent), is not recommended. Originality/value - This study is the first one, as far as it is known, to identify the scenarios under which the methods for estimating the VaR confidence intervals perform properly. The findings are supported by simulation and empirical exercises.

Suggested Citation

  • Santiago Gamba-Santamaria & Oscar Fernando Jaulin-Mendez & Luis Fernando Melo-Velandia & Carlos Andrés Quicazán-Moreno, 2016. "Comparison of methods for estimating the uncertainty of value at risk," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 33(4), pages 595-624, October.
    • Handle: RePEc:eme:sefpps:v:33:y:2016:i:4:p:595-624
    DOI: 10.1108/SEF-03-2016-0055
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    References listed on IDEAS

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    1. 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.
    2. Francq, Christian & Zakoïan, Jean-Michel, 2015. "Risk-parameter estimation in volatility models," Journal of Econometrics, Elsevier, vol. 184(1), pages 158-173.
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    4. 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.
    5. 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.
    6. 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.
    7. Christoffersen, Peter, 2011. "Elements of Financial Risk Management," Elsevier Monographs, Elsevier, edition 2, number 9780123744487.
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    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

    Confidence intervals; Data tilting; Hill estimator; Subsample bootstrap; Value at risk;
    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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