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Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures

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  • Gerlach, Richard
  • Wang, Chao

Abstract

This paper extends the joint Value-at-Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2019), by incorporating a realized measure to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Furthermore, we propose and test a new model for the dynamics of the ES component. Both a maximum likelihood and an adaptive Bayesian Markov chain Monte Carlo method are employed for estimation, the properties of which are compared in a simulation study. The results favour the Bayesian approach, which is employed subsequently in a forecasting study of seven financial market indices. The proposed models are compared to a range of parametric, non-parametric and semi-parametric competitors, including GARCH, realized GARCH, the extreme value theory method and the joint VaR and ES models of Taylor (2019), in terms of the accuracy of one-day-ahead VaR and ES forecasts, over a long forecast sample period that includes the global financial crisis in 2007–2008. The results are favorable for the proposed models incorporating a realized measure, especially when employing the sub-sampled realized variance and the sub-sampled realized range.

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  • Gerlach, Richard & Wang, Chao, 2020. "Semi-parametric dynamic asymmetric Laplace models for tail risk forecasting, incorporating realized measures," International Journal of Forecasting, Elsevier, vol. 36(2), pages 489-506.
    • Handle: RePEc:eee:intfor:v:36:y:2020:i:2:p:489-506
    DOI: 10.1016/j.ijforecast.2019.07.003
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    3. Lodge, David & Pérez, Javier J. & Albrizio, Silvia & Everett, Mary & De Bandt, Olivier & Georgiadis, Georgios & Ca' Zorzi, Michele & Lastauskas, Povilas & Carluccio, Juan & Parrága, Susana & Carvalho,, 2021. "The implications of globalisation for the ECB monetary policy strategy," Occasional Paper Series 263, European Central Bank.
    4. Vincenzo Candila & Giampiero M. Gallo & Lea Petrella, 2020. "Mixed--frequency quantile regressions to forecast Value--at--Risk and Expected Shortfall," Papers 2011.00552, arXiv.org, revised Mar 2023.
    5. Li, Dan & Clements, Adam & Drovandi, Christopher, 2023. "A Bayesian approach for more reliable tail risk forecasts," Journal of Financial Stability, Elsevier, vol. 64(C).
    6. Timo Dimitriadis & Tobias Fissler & Johanna Ziegel, 2020. "The Efficiency Gap," Papers 2010.14146, arXiv.org, revised Sep 2022.
    7. Dimitriadis, Timo & Liu, Xiaochun & Schnaitmann, Julie, 2020. "Encompassing tests for value at risk and expected shortfall multi-step forecasts based on inference on the boundary," Hohenheim Discussion Papers in Business, Economics and Social Sciences 11-2020, University of Hohenheim, Faculty of Business, Economics and Social Sciences.
    8. Cathy W. S. Chen & Takaaki Koike & Wei-Hsuan Shau, 2024. "Tail risk forecasting with semi-parametric regression models by incorporating overnight information," Papers 2402.07134, arXiv.org.
    9. H. Rangika Iroshani Peiris & Chao Wang & Richard Gerlach & Minh-Ngoc Tran, 2024. "Semi-parametric financial risk forecasting incorporating multiple realized measures," Papers 2402.09985, arXiv.org.
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    12. Taylor, James W., 2021. "Evaluating quantile-bounded and expectile-bounded interval forecasts," International Journal of Forecasting, Elsevier, vol. 37(2), pages 800-811.
    13. Lazar, Emese & Wang, Shixuan & Xue, Xiaohan, 2023. "Loss function-based change point detection in risk measures," European Journal of Operational Research, Elsevier, vol. 310(1), pages 415-431.
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