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Estimation-Adjusted Var

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Author Info

  • Gourieroux, Christian
  • Zakoïan, Jean-Michel

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

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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 29 (2013)
Issue (Month): 04 (August)
Pages: 735-770

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Handle: RePEc:cup:etheor:v:29:y:2013:i:04:p:735-770_00

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  1. 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.
  2. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
  3. 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.
  4. Marcus J Chambers, 2010. "Jackknife Estimation of Stationary Autoregressive Models," Economics Discussion Papers 684, University of Essex, Department of Economics.
  5. Bao, Yong & Ullah, Aman, 2004. "Bias of a Value-at-Risk estimator," Finance Research Letters, Elsevier, vol. 1(4), pages 241-249, December.
  6. Dufour, J.M. & Kiviet, J.F., 1995. "Exact Tests in Single Equation Autoregressive Distributed Lag Models," Cahiers de recherche 9549, Universite de Montreal, Departement de sciences economiques.
  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, Society for Financial Econometrics, 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 04:19:00
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Cited by:
  1. Christophe Hurlin & Sebastien Laurent & Rogier Quaedvlieg & Stephan Smeekes, 2013. "Risk Measure Inference," Working Papers halshs-00877279, HAL.

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