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A residual bootstrap for conditional Value-at-Risk

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  • Beutner, Eric
  • Heinemann, Alexander
  • Smeekes, Stephan

Abstract

A fixed-design residual bootstrap method is proposed for the two-step estimator of Francq and Zakoïan(2015) associated with the conditional Value-at-Risk. The bootstrap’s consistency is proven for a general class of volatility models and intervals are constructed for the conditional Value-at-Risk. A simulation study reveals that the equal-tailed percentile bootstrap interval tends to fall short of its nominal value. In contrast, the reversed-tails bootstrap interval yields accurate coverage. We also compare the theoretically analyzed fixed-design bootstrap with the recursive-design bootstrap. It turns out that the fixed-design bootstrap performs equally well in terms of average coverage, yet leads on average to shorter intervals in smaller samples. An empirical application illustrates the interval estimation.

Suggested Citation

  • Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    • Handle: RePEc:eee:econom:v:238:y:2024:i:2:s0304407623002701
    DOI: 10.1016/j.jeconom.2023.105554
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    Cited by:

    1. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    2. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    3. Francq, Christian & Zakoïan, Jean-Michel, 2022. "Testing the existence of moments for GARCH processes," Journal of Econometrics, Elsevier, vol. 227(1), pages 47-64.
    4. Eric Beutner & Julia Schaumburg & Barend Spanjers, 2024. "Bootstrapping GARCH Models Under Dependent Innovations," Tinbergen Institute Discussion Papers 24-008/III, Tinbergen Institute.
    5. Cavaliere, Giuseppe & Nielsen, Heino Bohn & Pedersen, Rasmus Søndergaard & Rahbek, Anders, 2022. "Bootstrap inference on the boundary of the parameter space, with application to conditional volatility models," Journal of Econometrics, Elsevier, vol. 227(1), pages 241-263.
    6. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    7. Royer, Julien, 2021. "Conditional asymmetry in Power ARCH($\infty$) models," MPRA Paper 109118, University Library of Munich, Germany.
    8. Alexander Heinemann, 2019. "A Bootstrap Test for the Existence of Moments for GARCH Processes," Papers 1902.01808, arXiv.org, revised Jul 2019.
    9. Heil, Thomas L.A. & Peter, Franziska J. & Prange, Philipp, 2022. "Measuring 25 years of global equity market co-movement using a time-varying spatial model," Journal of International Money and Finance, Elsevier, vol. 128(C).

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    More about this item

    Keywords

    Residual bootstrap; Value-at-Risk; GARCH;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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