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How valuable is your VaR? Large sample confidence intervals for normal VaR

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  • Moraux, Franck

Abstract

Little is known about the distribution of the ‘value-at-risk’ (VaR) estimate and the associated estimation risk. In the case of the normal VaR, the key problem comes from the fact that it is estimated using a couple of parameters whose estimates are distributed differently. Previous research has either neglected uncertainty around the mean parameter, or resorted to simulations. By contrast, this paper derives analytical results for the normal VaR with the help of asymptotic theory and the so-called ‘delta method’. Properties of the estimation errors are then explored in detail and the VaR estimation risk is broken down into its various components. It is then shown, among other things, that the fraction of error owing to mean uncertainty is limited in a prudential context. In other words, the approximate approach defended by Jorion and Chappell and Dowd is shown to still be relevant.

Suggested Citation

  • 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.
    • Handle: RePEc:aza:rmfi00:y:2011:v:4:i:2:p:189-200
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    Cited by:

    1. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.
    2. 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.
    3. Santiago Gamba Santamaría & Oscar Fernando Jaulín Méndez & Luis Fernando Melo Velandia & Carlos Andrés Quicazán Moreno, 2015. "Comparación De Métodos Para La Estimación De La Incertidumbre Del Valor En Riesgo," Temas de Estabilidad Financiera 83, Banco de la Republica de Colombia.
    4. Marouane Airouss & Mohamed Tahiri & Amale Lahlou & Abdelhak Hassouni, 2018. "Advanced Expected Tail Loss Measurement and Quantification for the Moroccan All Shares Index Portfolio," Mathematics, MDPI, vol. 6(3), pages 1-19, March.
    5. Silvia Stanescu & Radu Tunaru, 2013. "Quantifying the uncertainty in VaR and expected shortfall estimates," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 15, pages 357-372, Edward Elgar Publishing.
    6. 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.
    7. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.

    More about this item

    Keywords

    value-at-risk; estimation risk; confidence interval; large sample;
    All these keywords.

    JEL classification:

    • G2 - Financial Economics - - Financial Institutions and Services
    • E5 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit

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