IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v34y2018i01p23-67_00.html

Nonparametric Estimation Of Conditional Value-At-Risk And Expected Shortfall Based On Extreme Value Theory

Author

Listed:
  • Martins-Filho, Carlos
  • Yao, Feng
  • Torero, Maximo

Abstract

We propose nonparametric estimators for conditional value-at-risk (CVaR) and conditional expected shortfall (CES) 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 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, Annals of Statistics 3, 119–131) to give final estimators for CVaR and CES. We provide consistency and asymptotic normality of the proposed estimators under suitable normalization. We also 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

  • 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.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:01:p:23-67_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466616000517/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    3. Christis Katsouris, 2023. "Quantile Time Series Regression Models Revisited," Papers 2308.06617, arXiv.org, revised Aug 2023.
    4. 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.
    5. 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.
    6. 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.
    7. Katerina Rigana & Ernst C. Wit & Samantha Cook, 2024. "Navigating Market Turbulence: Insights from Causal Network Contagion Value at Risk," Papers 2402.06032, arXiv.org.
    8. Stéphane Girard & Gilles Claude Stupfler & Antoine Usseglio-Carleve, 2021. "Extreme Conditional Expectile Estimation in Heavy-Tailed Heteroscedastic Regression Models," Post-Print hal-03306230, HAL.
    9. 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.
    10. 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.
    11. Yannick Hoga, 2023. "The Estimation Risk in Extreme Systemic Risk Forecasts," Papers 2304.10349, arXiv.org.
    12. 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.
    13. Alexander Heinemann & Sean Telg, 2018. "A Residual Bootstrap for Conditional Expected Shortfall," Papers 1811.11557, arXiv.org.
    14. 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).
    15. Ma, Yaolan & Wei, Bo, 2025. "Extreme conditional tail risk inference in ARMA–GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 177(C).
    16. Li, Yizhou & Polak, Paweł, 2025. "Asymptotic normality of the Conditional Value-at-Risk based Pickands estimator," Statistics & Probability Letters, Elsevier, vol. 223(C).
    17. 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.
    18. 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.
    19. 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.
    20. 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).
    21. 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.
    22. 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.
    23. Denis Chetverikov & Yukun Liu & Aleh Tsyvinski, 2022. "Weighted-average quantile regression," Papers 2203.03032, arXiv.org.
    24. 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.

    More about this item

    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)

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:34:y:2018:i:01:p:23-67_00. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.