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Evaluating Value-at-Risk forecasts: A new set of multivariate backtests

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  • Wied, Dominik
  • Weiß, Gregor N.F.
  • Ziggel, Daniel

Abstract

We propose two new tests for detecting clustering in multivariate Value-at-Risk (VaR) forecasts. First, we consider CUSUM-tests to detect non-constant expectations in the matrix of VaR-violations. Second, we propose χ2-tests for detecting cross-sectional and serial dependence in the VaR-forecasts. Moreover, we combine our new backtests with a test of unconditional coverage to yield two new backtests of multivariate conditional coverage. Results from a simulation study underline the usefulness of our new backtests for controlling portfolio risks across a bank’s business lines. In an empirical study, we show how our multivariate backtests can be employed by regulators to backtest a banking system.

Suggested Citation

  • Wied, Dominik & Weiß, Gregor N.F. & Ziggel, Daniel, 2016. "Evaluating Value-at-Risk forecasts: A new set of multivariate backtests," Journal of Banking & Finance, Elsevier, vol. 72(C), pages 121-132.
    • Handle: RePEc:eee:jbfina:v:72:y:2016:i:c:p:121-132
    DOI: 10.1016/j.jbankfin.2016.07.014
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    References listed on IDEAS

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    Cited by:

    1. Nikola RADIVOJEVIĆ & Luka FILIPOVI & Тomislav D. BRZAKOVIĆ, 2020. "A New Semiparametric Mirrored Historical Simulation Value-At-Risk Model," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(1), pages 5-21, March.
    2. Thiele, Stephen, 2019. "Detecting underestimates of risk in VaR models," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 12-20.
    3. Denisa Banulescu-Radu & Christophe Hurlin & Jérémy Leymarie & Olivier Scaillet, 2021. "Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures," Management Science, INFORMS, vol. 67(9), pages 5730-5754, September.
    4. Holger Fink & Andreas Fuest & Henry Port, 2018. "The Impact of Sovereign Yield Curve Differentials on Value-at-Risk Forecasts for Foreign Exchange Rates," Risks, MDPI, vol. 6(3), pages 1-19, August.
    5. Marta Małecka, 2021. "Testing for a serial correlation in VaR failures through the exponential autoregressive conditional duration model," Statistics in Transition New Series, Polish Statistical Association, vol. 22(1), pages 145-162, March.
    6. Kratz, Marie & Lok, Yen H. & McNeil, Alexander J., 2018. "Multinomial VaR backtests: A simple implicit approach to backtesting expected shortfall," Journal of Banking & Finance, Elsevier, vol. 88(C), pages 393-407.
    7. Gordy, Michael B. & McNeil, Alexander J., 2020. "Spectral backtests of forecast distributions with application to risk management," Journal of Banking & Finance, Elsevier, vol. 116(C).
    8. Jean-Paul Laurent & Hassan Omidi Firouzi, 2022. "Market Risk and Volatility Weighted Historical Simulation After Basel III," Working Papers hal-03679434, HAL.
    9. Leung, Melvern & Li, Youwei & Pantelous, Athanasios A. & Vigne, Samuel A., 2021. "Bayesian Value-at-Risk backtesting: The case of annuity pricing," European Journal of Operational Research, Elsevier, vol. 293(2), pages 786-801.
    10. Codrut Florin Ivascu & Daniela Serban, 2023. "Value at Risk Estimation for Non-Gaussian Distributions," The Review of Finance and Banking, Academia de Studii Economice din Bucuresti, Romania / Facultatea de Finante, Asigurari, Banci si Burse de Valori / Catedra de Finante, vol. 15(2), pages 181-190, December.
    11. Małecka Marta, 2021. "Testing for a serial correlation in VaR failures through the exponential autoregressive conditional duration model," Statistics in Transition New Series, Polish Statistical Association, vol. 22(1), pages 145-162, March.

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    More about this item

    Keywords

    Model risk; Multivariate backtesting; Value-at-Risk; Systemic risk;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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