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Evaluating the accuracy of value-at-risk forecasts: New multilevel tests

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  • Leccadito, Arturo
  • Boffelli, Simona
  • Urga, Giovanni

Abstract

We propose independence and conditional coverage tests which are aimed at evaluating the accuracy of Value-at-Risk (VaR) forecasts from the same model at different confidence levels. The proposed procedures are multilevel tests, i.e., joint tests of several quantiles corresponding to different confidence levels. In a comprehensive Monte Carlo exercise, we document the superiority of the proposed tests with respect to existing multilevel tests. In an empirical application, we illustrate the implementation of the tests using several VaR models and daily data for 15 MSCI world indices.

Suggested Citation

  • Leccadito, Arturo & Boffelli, Simona & Urga, Giovanni, 2014. "Evaluating the accuracy of value-at-risk forecasts: New multilevel tests," International Journal of Forecasting, Elsevier, vol. 30(2), pages 206-216.
    • Handle: RePEc:eee:intfor:v:30:y:2014:i:2:p:206-216
    DOI: 10.1016/j.ijforecast.2013.07.014
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    Cited by:

    1. 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.
    2. Laura Garcia‐Jorcano & Alfonso Novales, 2021. "Volatility specifications versus probability distributions in VaR forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(2), pages 189-212, March.
    3. Lazar, Emese & Zhang, Ning, 2019. "Model risk of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 74-93.
    4. Boucher, Christophe M. & Daníelsson, Jón & Kouontchou, Patrick S. & Maillet, Bertrand B., 2014. "Risk models-at-risk," Journal of Banking & Finance, Elsevier, vol. 44(C), pages 72-92.
    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. Zhi-Fu Mi & Yi-Ming Wei & Bao-Jun Tang & Rong-Gang Cong & Hao Yu & Hong Cao & Dabo Guan, 2017. "Risk assessment of oil price from static and dynamic modelling approaches," Applied Economics, Taylor & Francis Journals, vol. 49(9), pages 929-939, February.
    7. Marta Małecka & Radosław Pietrzyk, 2024. "A spectral approach to evaluating VaR forecasts: stock market evidence from the subprime mortgage crisis, through COVID-19, to the Russo–Ukrainian war," Quality & Quantity: International Journal of Methodology, Springer, vol. 58(5), pages 4533-4567, October.
    8. 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).
    9. Andrés Eduardo Jiménez Gómez & Luis Fernando Melo Velandia, 2014. "Modelación de la asimetría y curtosis condicionales: una aplicación VaR para series colombianas," Borradores de Economia 834, Banco de la Republica de Colombia.
    10. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    11. Jean-Paul Laurent & Hassan Omidi Firouzi, 2022. "Market Risk and Volatility Weighted Historical Simulation After Basel III," Working Papers hal-03679434, HAL.
    12. Marta Małecka, 2024. "New runs‐based approach to testing value at risk forecasts," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(6), pages 2021-2041, September.
    13. Luis Melo Velandia & Luis Fernando Melo Velandia, 2019. "Regresión cuantílica dinámica para la medición del valor en riesgo: Una aplicación a datos colombianos," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, vol. 38(76), pages 23-50, January.
    14. Santiago Gamba-Santamaria & Oscar Fernando Jaulin-Mendez & Luis Fernando Melo-Velandia & Carlos Andrés Quicazán-Moreno, 2016. "Comparison of methods for estimating the uncertainty of value at risk," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 33(4), pages 595-624, October.
    15. Laura Garcia-Jorcano & Alfonso Novales, 2020. "A dominance approach for comparing the performance of VaR forecasting models," Computational Statistics, Springer, vol. 35(3), pages 1411-1448, September.
    16. Argyropoulos, Christos & Panopoulou, Ekaterini, 2019. "Backtesting VaR and ES under the magnifying glass," International Review of Financial Analysis, Elsevier, vol. 64(C), pages 22-37.
    17. Małecka Marta, 2021. "Testing for a serial correlation in VaR failures through the exponential autoregressive conditional duration model," Statistics in Transition New Series, Statistics Poland, vol. 22(1), pages 145-162, March.
    18. Georges Tsafack & James Cataldo, 2021. "Backtesting and estimation error: value-at-risk overviolation rate," Empirical Economics, Springer, vol. 61(3), pages 1351-1396, September.

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