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Estimation-Adjusted Var

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  • 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 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

  • Gourieroux, Christian & Zakoïan, Jean-Michel, 2013. "Estimation-Adjusted Var," Econometric Theory, Cambridge University Press, vol. 29(4), pages 735-770, August.
    • Handle: RePEc:cup:etheor:v:29:y:2013:i:04:p:735-770_00
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    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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    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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