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Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics

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  • Chun, So Yeon
  • Shapiro, Alexander
  • Uryasev, Stan

Abstract

We discuss linear regression approaches to conditional Value-at-Risk and Average Value-at-Risk (Conditional Value-at-Risk, Expected Shortfall) risk measures. Two estimation procedures are considered for each conditional risk measure, one is direct and the other is based on residual analysis of the standard least squares method. Large sample statistical inference of the estimators obtained is derived. Furthermore, finite sample properties of the proposed estimators are investigated and compared with theoretical derivations in an extensive Monte Carlo study. Empirical results on the real-data (different financial asset classes) are also provided to illustrate the performance of the estimators.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 30132.

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Date of creation: 03 Apr 2011
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Handle: RePEc:pra:mprapa:30132

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Keywords: Value-at-Risk; Average Value-at-Risk; Conditional Value-at-Risk; Expected Shortfall; linear regression; least squares residual; quantile regression; conditional risk measures; statistical inference;

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References

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  1. Trindade, A. Alexandre & Uryasev, Stan & Shapiro, Alexander & Zrazhevsky, Grigory, 2007. "Financial prediction with constrained tail risk," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3524-3538, November.
  2. 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.
  3. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
  4. Olivier SCAILLET, 2004. "Nonparametric Estimation of Conditional Expected Shortfall," FAME Research Paper Series rp112, International Center for Financial Asset Management and Engineering.
  5. 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.
  6. 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.
  7. 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.
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  9. Jackson, Patricia & Perraudin, William, 2000. "Regulatory implications of credit risk modelling," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 1-14, January.
  10. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
  11. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  12. Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
  13. 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.
  14. Jeremy Berkowitz & James O'Brien, 2002. "How Accurate Are Value-at-Risk Models at Commercial Banks?," Journal of Finance, American Finance Association, vol. 57(3), pages 1093-1111, 06.
  15. Franco Peracchi & Andrei V. Tanase, 2008. "On estimating the conditional expected shortfall," CEIS Research Paper 122, Tor Vergata University, CEIS, revised 14 Jul 2008.
  16. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129.
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Cited by:
  1. Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
  2. Fabrice Gamboa & Aur\'elien Garivier & Bertrand Iooss & Tatiana Labopin-Richard, 2014. "Bregman superquantiles. Estimation methods and applications," Papers 1405.6677, arXiv.org.

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