IDEAS home Printed from https://ideas.repec.org/p/crs/wpaper/2012-16.html
   My bibliography  Save this paper

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
    as

    Download full text from publisher

    File URL: http://crest.science/RePEc/wpstorage/2012-16.pdf
    File Function: Crest working paper version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    2. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value‐at‐Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, June.
    3. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Ophélie Couperier & Jérémy Leymarie, 2020. "Backtesting Expected Shortfall via Multi-Quantile Regression," Working Papers halshs-01909375, HAL.
    4. 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.
    5. 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.
    6. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
    2. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    3. Claußen, Arndt & Rösch, Daniel & Schmelzle, Martin, 2019. "Hedging parameter risk," Journal of Banking & Finance, Elsevier, vol. 100(C), pages 111-121.
    4. 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, December.
    5. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    6. 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.
    7. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    8. Köksal, Bülent & Orhan, Mehmet, 2012. "Market risk of developed and developing countries during the global financial crisis," MPRA Paper 37523, University Library of Munich, Germany.
    9. Escanciano, Juan Carlos & Pei, Pei, 2012. "Pitfalls in backtesting Historical Simulation VaR models," Journal of Banking & Finance, Elsevier, vol. 36(8), pages 2233-2244.
    10. Carl Lonnbark, 2010. "A corrected Value-at-Risk predictor," Applied Economics Letters, Taylor & Francis Journals, vol. 17(12), pages 1193-1196.
    11. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    12. Elena-Ivona DUMITRESCU, 2011. "Backesting Value-at-Risk: From DQ (Dynamic Quantile) to DB (Dynamic Binary) Tests," LEO Working Papers / DR LEO 262, Orleans Economics Laboratory / Laboratoire d'Economie d'Orleans (LEO), University of Orleans.
    13. Thiele, Stephen, 2019. "Detecting underestimates of risk in VaR models," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 12-20.
    14. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    15. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    16. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    17. Sander Barendse & Erik Kole & Dick van Dijk, 2023. "Backtesting Value-at-Risk and Expected Shortfall in the Presence of Estimation Error," Journal of Financial Econometrics, Oxford University Press, vol. 21(2), pages 528-568.
    18. El Bouhadi, Abdelhamid & Achibane, Khalid, 2009. "The Predictive Power of Conditional Models: What Lessons to Draw with Financial Crisis in the Case of Pre-Emerging Capital Markets?," MPRA Paper 19482, University Library of Munich, Germany.
    19. Sylvain Benoit & Christophe Hurlin & Christophe Perignon, 2015. "Implied Risk Exposures," Review of Finance, European Finance Association, vol. 19(6), pages 2183-2222.
    20. 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).

    More about this item

    Keywords

    Value-at-Risk; Estimation Risk; Bias Correction; ARCH Model;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:crs:wpaper:2012-16. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Secretariat General (email available below). General contact details of provider: https://edirc.repec.org/data/crestfr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.