Conditional Value-at-Risk and Average Value-at-Risk: Estimation and Asymptotics
AbstractWe 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 InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 30132.
Date of creation: 03 Apr 2011
Date of revision:
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;
Find related papers by JEL classification:
- C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
- G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-04-23 (All new papers)
- NEP-BAN-2011-04-23 (Banking)
- NEP-ECM-2011-04-23 (Econometrics)
- NEP-ORE-2011-04-23 (Operations Research)
- NEP-RMG-2011-04-23 (Risk Management)
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- 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.
- 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.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- 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.
- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- 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.
- 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.
- 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.
- 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.
- Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
- Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
- Jackson, Patricia & Perraudin, William, 2000. "Regulatory implications of credit risk modelling," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 1-14, January.
- 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.
- O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 115-129.
- Olivier SCAILLET, 2004. "Nonparametric Estimation of Conditional Expected Shortfall," FAME Research Paper Series rp112, International Center for Financial Asset Management and Engineering.
- 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.
- Franco Peracchi & Andrei V. Tanase, 2008. "On estimating the conditional expected shortfall," CEIS Research Paper 122, Tor Vergata University, CEIS, revised 14 Jul 2008.
- Fabrice Gamboa & Aur\'elien Garivier & Bertrand Iooss & Tatiana Labopin-Richard, 2014. "Bregman superquantiles. Estimation methods and applications," Papers 1405.6677, arXiv.org.
- Johanna F. Ziegel, 2013. "Coherence and elicitability," Papers 1303.1690, arXiv.org, revised Mar 2014.
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