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Estimation Adjusted VaR

Author Info

Listed author(s):
  • 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

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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2012-16.

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Length: 41
Date of creation: Sep 2012
Handle: RePEc:crs:wpaper:2012-16
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Keywords: Value-at-Risk; Estimation Risk; Bias Correction; ARCH Model;

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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.
  2. 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.
  3. Chambers, Marcus J., 2013. "Jackknife estimation of stationary autoregressive models," Journal of Econometrics, Elsevier, vol. 172(1), pages 142-157.
  4. 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.
  5. 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.
  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. Bao, Yong & Ullah, Aman, 2004. "Bias of a Value-at-Risk estimator," Finance Research Letters, Elsevier, vol. 1(4), pages 241-249, December.
  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 & Sébastien Laurent & Rogier Quaedvlieg & Stephan Smeekes, 2015. "Risk Measure Inference," Post-Print hal-01457393, HAL.
  2. 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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