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Estimation Adjusted VaR

Author

Listed:
  • Christian Gouriéroux

    (Crest et Université de Toronto)

  • Jean-Michel Zakoian

    (Canada et University Lille 3)

Abstract

Standard risk measures, such as the Value-at-Risk (VaR), or the Expected Shortfall, have to be estimated and their estimated counterparts are subject to estimation uncertainty. Replacing, in the theoretical formulas, the true parameter value by an estimator based on n observations of the Profit and Loss variable, induces an asymptotic bias of order 1/n in the coverage probabilities. This paper shows how to correct for this bias by introducing a new estimator of the VaR, called Estimation adjusted VaR (EVaR). This adjustment allows for a joint treatment of theoretical and estimation risks, taking into account for their possible dependence. The estimator is derived for a general parametric dynamic model and is particularized to stochastic drift and volatility models. The finite sample properties of the EVaR estimator are studied by simulation and an empirical study of the S&P Index is proposed

Suggested Citation

  • Christian Gouriéroux & Jean-Michel Zakoian, 2012. "Estimation Adjusted VaR," Working Papers 2012-16, Center for Research in Economics and Statistics.
  • Handle: RePEc:crs:wpaper:2012-16
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    References listed on IDEAS

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    1. Kiviet, Jan F. & Dufour, Jean-Marie, 1997. "Exact tests in single equation autoregressive distributed lag models," Journal of Econometrics, Elsevier, vol. 80(2), pages 325-353, October.
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    4. Bao, Yong & Ullah, Aman, 2004. "Bias of a Value-at-Risk estimator," Finance Research Letters, Elsevier, vol. 1(4), pages 241-249, December.
    5. 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.
    6. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    7. Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
    8. J. Carlos Escanciano & Jose Olmo, 2011. "Robust Backtesting Tests for Value-at-risk Models," Journal of Financial Econometrics, Oxford University Press, vol. 9(1), pages 132-161, Winter.
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    Blog mentions

    As found by EconAcademics.org, the blog aggregator for Economics research:
    1. What I Learned Last Week
      by Dave Giles in Econometrics Beat: Dave Giles' Blog on 2012-10-13 09:19:00

    Citations

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    Cited by:

    1. Farkas, Walter & Fringuellotti, Fulvia & Tunaru, Radu, 2020. "A cost-benefit analysis of capital requirements adjusted for model risk," Journal of Corporate Finance, Elsevier, vol. 65(C).
    2. Wang, Zheqi & Crook, Jonathan & Andreeva, Galina, 2020. "Reducing estimation risk using a Bayesian posterior distribution approach: Application to stress testing mortgage loan default," European Journal of Operational Research, Elsevier, vol. 287(2), pages 725-738.
    3. Christophe Hurlin & Sébastien Laurent & Rogier Quaedvlieg & Stephan Smeekes, 2017. "Risk Measure Inference," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(4), pages 499-512, October.
    4. Gourieroux, Christian & Tiomo, Andre, 2019. "The Evaluation of Model Risk for Probability of Default and Expected Loss," MPRA Paper 95795, University Library of Munich, Germany.
    5. Ophélie Couperier & Jérémy Leymarie, 2020. "Backtesting Expected Shortfall via Multi-Quantile Regression," Working Papers halshs-01909375, HAL.
    6. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.

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    More about this item

    Keywords

    Value-at-Risk; Estimation Risk; Bias Correction; ARCH Model;
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