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Estimation of Value-at-Risk and Expected Shortfall based on Nonlinear Models of Return Dynamics and Extreme Value Theory

Author

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  • Martins-Filho Carlos

    (Oregon State University)

  • Yao Feng

    (University of North Dakota)

Abstract

We propose an estimation procedure for value-at-risk (VaR) and expected shortfall (TailVaR) for conditional distributions of a time series of returns on a financial asset. Our approach combines a local polynomial estimator of conditional mean and volatility functions in a conditional heterocedastic autoregressive nonlinear (CHARN) model with Extreme Value Theory for estimating quantiles of the conditional distribution. We investigate the finite sample properties of our method and contrast them with alternatives, including the method recently proposed by McNeil and Frey (2000), in an extensive Monte Carlo study. The method we propose outperforms the estimators currently available in the literature. An evaluation based on backtesting was also performed.

Suggested Citation

  • Martins-Filho Carlos & Yao Feng, 2006. "Estimation of Value-at-Risk and Expected Shortfall based on Nonlinear Models of Return Dynamics and Extreme Value Theory," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 10(2), pages 1-43, May.
    • Handle: RePEc:bpj:sndecm:v:10:y:2006:i:2:n:4
    DOI: 10.2202/1558-3708.1304
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    References listed on IDEAS

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    Cited by:

    1. Sofiane Aboura, 2014. "When the U.S. Stock Market Becomes Extreme?," Risks, MDPI, vol. 2(2), pages 1-15, May.
    2. Nieto, María Rosa, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," DES - Working Papers. Statistics and Econometrics. WS ws087326, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. 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".
    4. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    5. Emmanuel Jurczenko & Bertrand Maillet & Paul Merlin, 2008. "Efficient Frontier for Robust Higher-order Moment Portfolio Selection," Post-Print halshs-00336475, HAL.
    6. 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.
    7. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    8. Benjamin Mögel & Benjamin R. Auer, 2018. "How accurate are modern Value-at-Risk estimators derived from extreme value theory?," Review of Quantitative Finance and Accounting, Springer, vol. 50(4), pages 979-1030, May.
    9. Martins-Filho, Carlos & Yao, Feng, 2009. "Nonparametric regression estimation with general parametric error covariance," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 309-333, March.
    10. 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.
    11. Benjamin R. Auer & Benjamin Mögel, 2016. "How Accurate are Modern Value-at-Risk Estimators Derived from Extreme Value Theory?," CESifo Working Paper Series 6288, CESifo.
    12. Juan Carlos Escanciano & Jose Olmo, 2007. "Backtesting Parametric Value-at-Risk with Estimation Risk Abstract: One of the implications of the creation of Basel Committee on Banking Supervision was the implementation of Value-at-Risk (VaR) as t," Caepr Working Papers 2007-005, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
    13. Martins-Filho, Carlos & Yao, Feng & Torero, Maximo, 2018. "Nonparametric Estimation Of Conditional Value-At-Risk And Expected Shortfall Based On Extreme Value Theory," Econometric Theory, Cambridge University Press, vol. 34(1), pages 23-67, February.
    14. Giannopoulos, Kostas & Tunaru, Radu, 2005. "Coherent risk measures under filtered historical simulation," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 979-996, April.
    15. John G. Galbraith & Serguei Zernov, 2006. "Extreme Dependence In The Nasdaq And S&P Composite Indexes," Departmental Working Papers 2006-14, McGill University, Department of Economics.
    16. 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.
    17. Geenens, Gery & Dunn, Richard, 2022. "A nonparametric copula approach to conditional Value-at-Risk," Econometrics and Statistics, Elsevier, vol. 21(C), pages 19-37.

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