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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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    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

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    7. 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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