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ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES

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  • Gao, Feng
  • Song, Fengming

Abstract

Value-at-risk (VaR) and expected shortfall (ES) are now both widely used risk measures. However, users have not paid much attention to the estimation risk issues, especially in the case of heteroskedastic financial time series. The key challenge arises from the fact that the estimated generalized autoregressive conditional heteroskedasticity (GARCH) innovations are not the true independent innovations. The purpose of this work is to provide an analytical method to assess the precision of conditional VaR and ES in the GARCH model estimated by the filtered historical simulation (FHS) method based on the asymptotic behavior of the residual empirical distribution function in GARCH processes. The proposed method is evaluated by simulation and proved valid.

Suggested Citation

  • Gao, Feng & Song, Fengming, 2008. "ESTIMATION RISK IN GARCH VaR AND ES ESTIMATES," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1404-1424, October.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:05:p:1404-1424_08
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    Cited by:

    1. Rangika Peiris & Chao Wang & Richard Gerlach & Minh-Ngoc Tran, 2024. "Semi-parametric financial risk forecasting incorporating multiple realized measures," Papers 2402.09985, arXiv.org, revised Dec 2024.
    2. Beutner, Eric & Heinemann, Alexander & Smeekes, Stephan, 2024. "A residual bootstrap for conditional Value-at-Risk," Journal of Econometrics, Elsevier, vol. 238(2).
    3. Zaichao Du & Pei Pei, 2020. "Backtesting portfolio value‐at‐risk with estimated portfolio weights," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 605-619, September.
    4. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
    5. 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.
    6. Tafakori, Laleh & Pourkhanali, Armin & Fard, Farzad Alavi, 2018. "Forecasting spikes in electricity return innovations," Energy, Elsevier, vol. 150(C), pages 508-526.
    7. Wang, Xiaoyu & Xie, Dejun & Jiang, Jingjing & Wu, Xiaoxia & He, Jia, 2017. "Value-at-Risk estimation with stochastic interest rate models for option-bond portfolios," Finance Research Letters, Elsevier, vol. 21(C), pages 10-20.
    8. Julia S. Mehlitz & Benjamin R. Auer, 2021. "Time‐varying dynamics of expected shortfall in commodity futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(6), pages 895-925, June.
    9. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2014. "Bank regulation and international financial stability: A case against the 2006 Basel framework for controlling tail risk in trading books," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 107-130.
    10. Dominique Guegan & Bertrand K. Hassani & Kehan Li, 2016. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Documents de travail du Centre d'Economie de la Sorbonne 16034rr, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Jan 2017.
    11. Dominique Guegan & Bertrand Hassani & Kehan Li, 2017. "Measuring risks in the extreme tail: The extreme VaR and its confidence interval," Post-Print halshs-01317391, HAL.
    12. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    13. Santiago Gamba Santamaría & Oscar Fernando Jaulín Méndez & Luis Fernando Melo Velandia & Carlos Andrés Quicazán Moreno, 2015. "Comparación De Métodos Para La Estimación De La Incertidumbre Del Valor En Riesgo," Temas de Estabilidad Financiera 83, Banco de la Republica de Colombia.
    14. Spierdijk, Laura, 2016. "Confidence intervals for ARMA–GARCH Value-at-Risk: The case of heavy tails and skewness," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 545-559.
    15. Timo Dimitriadis & Yannick Hoga, 2022. "Dynamic CoVaR Modeling," Papers 2206.14275, arXiv.org, revised Feb 2024.
    16. Giovanni Barone Adesi, 2016. "VaR and CVaR Implied in Option Prices," JRFM, MDPI, vol. 9(1), pages 1-6, February.
    17. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    18. Leong, Soon Heng & Urga, Giovanni, 2023. "A practical multivariate approach to testing volatility spillover," Journal of Economic Dynamics and Control, Elsevier, vol. 153(C).
    19. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    20. Pei Pei, 2010. "Backtesting Portfolio Value-at-Risk with Estimated Portfolio Weights," CAEPR Working Papers 2010-010, Center for Applied Economics and Policy Research, Department of Economics, Indiana University Bloomington.

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