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Conditional VAR and Expected Shortfall: A New Functional Approach

Author

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  • Frédéric Ferraty
  • Alejandro Quintela-Del-Río

Abstract

We estimate two well-known risk measures, the value-at-risk (VAR) and the expected shortfall, conditionally to a functional variable (i.e., a random variable valued in some semi(pseudo)-metric space). We use nonparametric kernel estimation for constructing estimators of these quantities, under general dependence conditions. Theoretical properties are stated whereas practical aspects are illustrated on simulated data: nonlinear functional and GARCH(1,1) models. Some ideas on bandwidth selection using bootstrap are introduced. Finally, an empirical example is given through data of the S&P 500 time series.

Suggested Citation

  • Frédéric Ferraty & Alejandro Quintela-Del-Río, 2016. "Conditional VAR and Expected Shortfall: A New Functional Approach," Econometric Reviews, Taylor & Francis Journals, vol. 35(2), pages 263-292, February.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:2:p:263-292
    DOI: 10.1080/07474938.2013.807107
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    Citations

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    Cited by:

    1. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    2. Rice, Gregory & Wirjanto, Tony & Zhao, Yuqian, 2020. "Forecasting value at risk with intra-day return curves," International Journal of Forecasting, Elsevier, vol. 36(3), pages 1023-1038.
    3. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.
    4. Gaoke Liao & Zhenghui Li & Ziqing Du & Yue Liu, 2019. "The Heterogeneous Interconnections between Supply or Demand Side and Oil Risks," Energies, MDPI, vol. 12(11), pages 1-17, June.
    5. d’Addona, Stefano & Khanom, Najrin, 2022. "Estimating tail-risk using semiparametric conditional variance with an application to meme stocks," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 241-260.
    6. Fatimah A. Almulhim & Mohammed B. Alamari & Mustapha Rachdi & Ali Laksaci, 2024. "Recursive Estimation of the Expectile-Based Shortfall in Functional Ergodic Time Series," Mathematics, MDPI, vol. 12(24), pages 1-17, December.
    7. Yue Liu & Hao Dong & Pierre Failler, 2019. "The Oil Market Reactions to OPEC’s Announcements," Energies, MDPI, vol. 12(17), pages 1-15, August.
    8. Yanqiong Liu & Zhenghui Li & Yanyan Yao & Hao Dong, 2021. "Asymmetry of Risk Evolution in Crude Oil Market: From the Perspective of Dual Attributes of Oil," Energies, MDPI, vol. 14(13), pages 1-22, July.
    9. Larbi Ait-Hennani & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Nonparametric Estimation of the Expected Shortfall Regression for Quasi-Associated Functional Data," Mathematics, MDPI, vol. 10(23), pages 1-23, November.
    10. Cerqueti, Roy & Giacalone, Massimiliano & Panarello, Demetrio, 2019. "A Generalized Error Distribution Copula-based method for portfolios risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 687-695.

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