Nonparametric estimation of conditional VaR and expected shortfall
AbstractThis paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data. We show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution, continuous, and differentiable, besides the good properties from both the double kernel local linear and weighted Nadaraya-Watson estimators. Moreover, an ad hoc data-driven fashion bandwidth selection method is proposed, based on the nonparametric version of the Akaike information criterion. Finally, an empirical study is carried out to illustrate the finite sample performance of the proposed estimators.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal Journal of Econometrics.
Volume (Year): 147 (2008)
Issue (Month): 1 (November)
Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom
Boundary effects Empirical likelihood Expected shortfall Local linear estimation Nonparametric smoothing Value-at-risk Weighted double kernel;
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Carrasco, Marine & Chen, Xiaohong, 2002. "Mixing And Moment Properties Of Various Garch And Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 18(01), pages 17-39, February.
- Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
- Mika Meitz & Pentti Saikkonen, 2007.
"Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models,"
Economics Series Working Papers
327, University of Oxford, Department of Economics.
- Meitz, Mika & Saikkonen, Pentti, 2008. "Ergodicity, Mixing, And Existence Of Moments Of A Class Of Markov Models With Applications To Garch And Acd Models," Econometric Theory, Cambridge University Press, vol. 24(05), pages 1291-1320, October.
- Meitz, Mika & Saikkonen, Pentti, 2004. "Ergodicity, mixing, and existence of moments of a class of Markov models with applications to GARCH and ACD models," Working Paper Series in Economics and Finance 573, Stockholm School of Economics, revised 20 Apr 2007.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- 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.
- Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
- Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Song Xi Chen, 2005. "Nonparametric Inference of Value-at-Risk for Dependent Financial Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 3(2), pages 227-255.
- Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(01), pages 169-192, February.
- Cai, Zongwu & Xu, Xiaoping, 2008. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1595-1608.
- Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1317-1334, July.
- O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129.
- Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(1), pages 87-107, Winter.
- Alemany, Ramon & Bolancé, Catalina & Guillén, Montserrat, 2013. "A nonparametric approach to calculating value-at-risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 255-262.
- Maria Rosa Nieto & Esther Ruiz, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," Statistics and Econometrics Working Papers ws087326, Universidad Carlos III, Departamento de Estadística y Econometría.
- Carlos Castro & Stijn Ferrari, 2011. "Measuring and testing for the systemically important financial institutions," DOCUMENTOS DE TRABAJO 008779, UNIVERSIDAD DEL ROSARIO.
- Chun, So Yeon & Shapiro, Alexander & Uryasev, Stan, 2011. "Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics," MPRA Paper 30132, University Library of Munich, Germany.
- Ramon Alemany & Catalina Bolancé & Montserrat Guillén, 2012. "Nonparametric estimation of Value-at-Risk," Working Papers XREAP2012-19, Xarxa de Referència en Economia Aplicada (XREAP), revised Oct 2012.
- Samantha Leorato & Franco Peracchi & Andrei V. Tanase, 2010.
"Asymptotically Efficient Estimation of the Conditional Expected Shortfall,"
EIEF Working Papers Series
1013, Einaudi Institute for Economics and Finance (EIEF), revised Dec 2010.
- Leorato, Samantha & Peracchi, Franco & Tanase, Andrei V., 2012. "Asymptotically efficient estimation of the conditional expected shortfall," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 768-784.
- Shih-Kang Chao & Wolfgang Karl Härdle & Weining Wang, 2012. "Quantile Regression in Risk Calibration," SFB 649 Discussion Papers SFB649DP2012-006, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Rockafellar, R.T. & Royset, J.O. & Miranda, S.I., 2014. "Superquantile regression with applications to buffered reliability, uncertainty quantification, and conditional value-at-risk," European Journal of Operational Research, Elsevier, vol. 234(1), pages 140-154.
- Alex Huang, 2013. "Value at risk estimation by quantile regression and kernel estimator," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 225-251, August.
- Ramon Alemany & Catalina Bolance & Montserrat Guillen, 2014. "Accounting for severity of risk when pricing insurance products," Working Papers 2014-05, Universitat de Barcelona, UB Riskcenter.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
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.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.