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Nonparametric estimation of conditional value-at-risk and expected shortfall based on extreme value theory

Author

Listed:
  • Carlos Martins-Filho

    (University of Colorado, Department of Economics)

  • Feng Yao

    (West Virginia University, College of Business and Economics)

  • Maximo Torero

    (IFPRI)

Abstract
We propose nonparametric estimators for conditional value-at-risk (VaR) and expected shortfall (ES) associated with conditional distributions of a series of returns on a financial asset. The return series and the conditioning covariates, which may include lagged returns and other exogenous variables, are assumed to be strong mixing and follow a fully nonparametric conditional location-scale model. First stage nonparametric estimators for location and scale are combined with a generalized Pareto approximation for distribution tails proposed by Pickands (1975) to give final estimators for conditional VaR and ES. We provide asymptotic characterizations of the proposed estimators and present the results of a Monte Carlo study that sheds light on their finite sample performance. Empirical viability of the model and estimators is investigated through a backtesting exercise using returns on future contracts for five agricultural commodities.

Suggested Citation

  • Carlos Martins-Filho & Feng Yao & Maximo Torero, 2012. "Nonparametric estimation of conditional value-at-risk and expected shortfall based on extreme value theory," Working Papers 13-05, Department of Economics, West Virginia University.
    • Handle: RePEc:wvu:wpaper:13-05
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    File URL: https://researchrepository.wvu.edu/cgi/viewcontent.cgi?article=1082&context=econ_working-papers
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    References listed on IDEAS

    as
    1. 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.
    2. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    3. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    4. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    5. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    6. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    7. Carlos Martins-Filho & Feng Yao & Maximo Torero, 2015. "High-Order Conditional Quantile Estimation Based on Nonparametric Models of Regression," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 907-958, December.
    8. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, September.
    9. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    10. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    11. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    12. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    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.
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    Cited by:

    1. Athanasios Triantafyllou & George Dotsis & Alexandros Sarris, 2020. "Assessing the Vulnerability to Price Spikes in Agricultural Commodity Markets," Journal of Agricultural Economics, Wiley Blackwell, vol. 71(3), pages 631-651, September.
    2. Gery Geenens & Richard Dunn, 2017. "A nonparametric copula approach to conditional Value-at-Risk," Papers 1712.05527, arXiv.org, revised Oct 2019.
    3. Emmanuel Torsen & Peter N. Mwita & Joseph K. Mungatu, 2018. "Nonparametric Estimation of the Error Functional of a Location-Scale Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 7(4), pages 1-1.
    4. Ji Hyung Lee & Yuya Sasaki & Alexis Akira Toda & Yulong Wang, 2021. "Fixed-k Tail Regression: New Evidence on Tax and Wealth Inequality from Forbes 400," Papers 2105.10007, arXiv.org, revised Sep 2022.
    5. Wilson Calmon & Eduardo Ferioli & Davi Lettieri & Johann Soares & Adrian Pizzinga, 2021. "An Extensive Comparison of Some Well‐Established Value at Risk Methods," International Statistical Review, International Statistical Institute, vol. 89(1), pages 148-166, April.
    6. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    7. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    8. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Inference for extremal regression with dependent heavy-tailed data," TSE Working Papers 22-1324, Toulouse School of Economics (TSE), revised 29 Aug 2023.
    9. Emmanuel Torsen & Peter N. Mwita & Joseph K. Mung’atu, 2019. "A Three-Step Nonparametric Estimation of Conditional Value-At-Risk Admitting a Location-Scale Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(4), pages 1-1.
    10. 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.
    11. Yuya Sasaki & Yulong Wang, 2022. "Fixed-k Inference for Conditional Extremal Quantiles," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 829-837, April.
    12. Cui, Zhenyu & Kirkby, J. Lars & Nguyen, Duy, 2021. "A data-driven framework for consistent financial valuation and risk measurement," European Journal of Operational Research, Elsevier, vol. 289(1), pages 381-398.
    13. Katerina Rigana & Ernst C. Wit & Samantha Cook, 2024. "Navigating Market Turbulence: Insights from Causal Network Contagion Value at Risk," Papers 2402.06032, arXiv.org.
    14. Stéphane Girard & Gilles Claude Stupfler & Antoine Usseglio-Carleve, 2021. "Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models," Post-Print hal-03306230, HAL.
    15. 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.
    16. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    17. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    18. Nicola Loperfido & Tomer Shushi, 2023. "Optimal Portfolio Projections for Skew-Elliptically Distributed Portfolio Returns," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 143-166, October.
    19. Denis Chetverikov & Yukun Liu & Aleh Tsyvinski, 2022. "Weighted-average quantile regression," Papers 2203.03032, arXiv.org.
    20. Yan Fang & Jian Li & Yinglin Liu & Yunfan Zhao, 2023. "Semiparametric estimation of expected shortfall and its application in finance," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(4), pages 835-851, July.
    21. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    22. Litimein, Ouahiba & Laksaci, Ali & Ait-Hennani, Larbi & Mechab, Boubaker & Rachdi, Mustapha, 2024. "Asymptotic normality of the local linear estimator of the functional expectile regression," Journal of Multivariate Analysis, Elsevier, vol. 202(C).

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    More about this item

    Keywords

    Value-at-risk; expected shortfall; extreme value theory; nonparametric location-scale models; strong mixing;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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