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Monitoring Value-at-Risk and Expected Shortfall Forecasts

Author

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  • Yannick Hoga

    (Faculty of Economics and Business Administration, University of Duisburg-Essen, D–45117 Essen, Germany)

  • Matei Demetrescu

    (Department of Statistics, TU Dortmund University, D–44221 Dortmund, Germany)

Abstract

This paper introduces formal monitoring procedures as a risk-management tool. Continuously monitoring risk forecasts allows practitioners to swiftly review and update their forecasting procedures as soon as forecasts turn inadequate. Similarly, regulators may take timely action in case reported risk forecasts become poor. Extant (one-shot) backtests require, however, that all data are available prior to testing and are not informative of when inadequacies might have occurred. To monitor value-at-risk and expected shortfall forecasts “online”—that is, as new observations become available—we construct sequential testing procedures. We derive the exact finite-sample distributions of the proposed procedures and discuss the suitability of asymptotic approximations. Simulations demonstrate good behavior of our exact procedures in finite samples. An empirical application to major stock indices during the COVID-19 pandemic illustrates the economic benefits of our monitoring approach.

Suggested Citation

  • Yannick Hoga & Matei Demetrescu, 2023. "Monitoring Value-at-Risk and Expected Shortfall Forecasts," Management Science, INFORMS, vol. 69(5), pages 2954-2971, May.
    • Handle: RePEc:inm:ormnsc:v:69:y:2023:i:5:p:2954-2971
    DOI: 10.1287/mnsc.2022.4460
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    References listed on IDEAS

    as
    1. Natalia Nolde & Johanna F. Ziegel, 2016. "Elicitability and backtesting: Perspectives for banking regulation," Papers 1608.05498, arXiv.org, revised Feb 2017.
    2. Bertrand Candelon & Gilbert Colletaz & Christophe Hurlin & Sessi Tokpavi, 2011. "Backtesting Value-at-Risk: A GMM Duration-Based Test," Journal of Financial Econometrics, Oxford University Press, vol. 9(2), pages 314-343, Spring.
    3. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    4. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
    5. Rustam Ibragimov, 2009. "Portfolio diversification and value at risk under thick-tailedness," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 565-580.
    6. Keith Kuester & Stefan Mittnik & Marc S. Paolella, 2006. "Value-at-Risk Prediction: A Comparison of Alternative Strategies," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 53-89.
    7. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
    8. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    9. Patton, Andrew J. & Ziegel, Johanna F. & Chen, Rui, 2019. "Dynamic semiparametric models for expected shortfall (and Value-at-Risk)," Journal of Econometrics, Elsevier, vol. 211(2), pages 388-413.
    10. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    11. Sebastian Bayer & Timo Dimitriadis, 2022. "Regression-Based Expected Shortfall Backtesting [Backtesting Expected Shortfall]," Journal of Financial Econometrics, Oxford University Press, vol. 20(3), pages 437-471.
    12. Jeremy Berkowitz & Peter Christoffersen & Denis Pelletier, 2011. "Evaluating Value-at-Risk Models with Desk-Level Data," Management Science, INFORMS, vol. 57(12), pages 2213-2227, December.
    13. Krämer, Walter & Wied, Dominik, 2015. "A simple and focused backtest of value at risk," Economics Letters, Elsevier, vol. 137(C), pages 29-31.
    14. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 84-108.
    15. Chavez-Demoulin, V. & Embrechts, P. & Sardy, S., 2014. "Extreme-quantile tracking for financial time series," Journal of Econometrics, Elsevier, vol. 181(1), pages 44-52.
    16. Ziggel, Daniel & Berens, Tobias & Weiß, Gregor N.F. & Wied, Dominik, 2014. "A new set of improved Value-at-Risk backtests," Journal of Banking & Finance, Elsevier, vol. 48(C), pages 29-41.
    17. Carmela Quintos & Zhenhong Fan & Peter C. B. Phillips, 2001. "Structural Change Tests in Tail Behaviour and the Asian Crisis," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(3), pages 633-663.
    18. Sven Otto & Jorg Breitung, 2020. "Backward CUSUM for Testing and Monitoring Structural Change with an Application to COVID-19 Pandemic Data," Papers 2003.02682, arXiv.org, revised Mar 2022.
    19. 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.
    20. Hang Chan, Ngai & Deng, Shi-Jie & Peng, Liang & Xia, Zhendong, 2007. "Interval estimation of value-at-risk based on GARCH models with heavy-tailed innovations," Journal of Econometrics, Elsevier, vol. 137(2), pages 556-576, April.
    21. Raffaella Giacomini & Barbara Rossi, 2010. "Forecast comparisons in unstable environments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 595-620.
    22. Berkes, István & Gombay, Edit & Horváth, Lajos & Kokoszka, Piotr, 2004. "SEQUENTIAL CHANGE-POINT DETECTION IN GARCH(p,q) MODELS," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1140-1167, December.
    23. Hoga, Yannick, 2017. "Monitoring multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 105-121.
    24. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    25. Fred Liu & Lars Stentoft, 2021. "Regulatory Capital and Incentives for Risk Model Choice under Basel 3 [Procyclical Leverage and Value-at-Risk]," Journal of Financial Econometrics, Oxford University Press, vol. 19(1), pages 53-96.
    26. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    27. Turan Bali & Panayiotis Theodossiou, 2007. "A conditional-SGT-VaR approach with alternative GARCH models," Annals of Operations Research, Springer, vol. 151(1), pages 241-267, April.
    28. Zaichao Du & Juan Carlos Escanciano, 2017. "Backtesting Expected Shortfall: Accounting for Tail Risk," Management Science, INFORMS, vol. 63(4), pages 940-958, April.
    29. Escanciano, J. Carlos & Olmo, Jose, 2010. "Backtesting Parametric Value-at-Risk With Estimation Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 36-51.
    30. Chu, Chia-Shang James & Stinchcombe, Maxwell & White, Halbert, 1996. "Monitoring Structural Change," Econometrica, Econometric Society, vol. 64(5), pages 1045-1065, September.
    31. Mauro Bernardi & Leopoldo Catania, 2016. "Comparison of Value-at-Risk models using the MCS approach," Computational Statistics, Springer, vol. 31(2), pages 579-608, June.
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    Cited by:

    1. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.

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