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Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data

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  • Jalal, Amine
  • Rockinger, Michael

Abstract

We investigate the consequences for Value-at-Risk and expected shortfall purposes of using a GARCH filter on various mis-specified processes. In general, we find that the McNeil and Frey (McNeil, A.J. and R. Frey, 2000, Estimation of Tail-Related Risk Measures for Heteroscedastic Financial Time Series: An Extreme Value Approach, Journal of Empirical Finance 7, 271-300.) two step procedure has very good forecasting properties. Using an unconditional non-filtered tail estimate also appears to perform satisfactorily for expected shortfall measurements but less so for VaR computations. Methods assuming specific densities such as the Gaussian or Student-t may yield wrong predictions. Thus, the use of an adequacy test for filtered data to given densities appears relevant. The paper builds on recent techniques to obtain thresholds for extreme value computations. Statistical tests for the expected shortfall, based on the circular bootstrap, are developed.

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  • Jalal, Amine & Rockinger, Michael, 2008. "Predicting tail-related risk measures: The consequences of using GARCH filters for non-GARCH data," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 868-877, December.
    • Handle: RePEc:eee:empfin:v:15:y:2008:i:5:p:868-877
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    8. Marco Bee & Debbie J. Dupuis & Luca Trapin, 2016. "US stock returns: are there seasons of excesses?," Quantitative Finance, Taylor & Francis Journals, vol. 16(9), pages 1453-1464, September.
    9. Tomlinson, Matthew F. & Greenwood, David & Mucha-Kruczyński, Marcin, 2024. "2T-POT Hawkes model for left- and right-tail conditional quantile forecasts of financial log returns: Out-of-sample comparison of conditional EVT models," International Journal of Forecasting, Elsevier, vol. 40(1), pages 324-347.
    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. J. Hambuckers & C. Heuchenne, 2017. "A robust statistical approach to select adequate error distributions for financial returns," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(1), pages 137-161, January.
    12. Majumder, Debasish, 2023. "Subjectivity in conventional tail measures: An exploratory model with 'risks & biases’," Finance Research Letters, Elsevier, vol. 55(PB).
    13. Weigert, Florian, 2013. "Crash Aversion and the Cross-Section of Expected Stock Returns Worldwide," Working Papers on Finance 1325, University of St. Gallen, School of Finance, revised Nov 2015.
    14. Bee, Marco & Dupuis, Debbie J. & Trapin, Luca, 2016. "Realizing the extremes: Estimation of tail-risk measures from a high-frequency perspective," Journal of Empirical Finance, Elsevier, vol. 36(C), pages 86-99.
    15. Huang, Alex YiHou, 2010. "An optimization process in Value-at-Risk estimation," Review of Financial Economics, Elsevier, vol. 19(3), pages 109-116, August.
    16. Alex YiHou Huang, 2010. "An optimization process in Value‐at‐Risk estimation," Review of Financial Economics, John Wiley & Sons, vol. 19(3), pages 109-116, August.
    17. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2015. "A comparison of Expected Shortfall estimation models," Journal of Economics and Business, Elsevier, vol. 78(C), pages 14-47.
    18. Taylor, James W., 2020. "Forecast combinations for value at risk and expected shortfall," International Journal of Forecasting, Elsevier, vol. 36(2), pages 428-441.
    19. Hamidreza Arian & Hossein Poorvasei & Azin Sharifi & Shiva Zamani, 2020. "The Uncertain Shape of Grey Swans: Extreme Value Theory with Uncertain Threshold," Papers 2011.06693, arXiv.org.
    20. Bertrand B. Maillet & Jean-Philippe R. M�decin, 2010. "Extreme Volatilities, Financial Crises and L-moment Estimations of Tail-indexes," Working Papers 2010_10, Department of Economics, University of Venice "Ca' Foscari".
    21. Riedel, Christoph & Wagner, Niklas, 2015. "Is risk higher during non-trading periods? The risk trade-off for intraday versus overnight market returns," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 39(C), pages 53-64.
    22. Quang Trinh, Vu & Duong Cao, Ngan & Li, Teng & Elnahass, Marwa, 2023. "Social capital, trust, and bank tail risk: The value of ESG rating and the effects of crisis shocks," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 83(C).

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    More about this item

    Keywords

    Extreme value theory Value-at-Risk (VaR) Expected shortfall GARCH Markov switching Jump diffusion Backtesting;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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