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Evaluating the Precision of Estimators of Quantile-Based Risk Measures

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  • Kevin Dowd
  • John Cotter

Abstract

This paper examines the precision of estimators of Quantile-Based Risk Measures (Value at Risk, Expected Shortfall, Spectral Risk Measures). It first addresses the question of how to estimate the precision of these estimators, and proposes a Monte Carlo method that is free of some of the limitations of existing approaches. It then investigates the distribution of risk estimators, and presents simulation results suggesting that the common practice of relying on asymptotic normality results might be unreliable with the sample sizes commonly available to them. Finally, it investigates the relationship between the precision of different risk estimators and the distribution of underlying losses (or returns), and yields a number of useful conclusions.

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File URL: http://arxiv.org/pdf/1103.5665
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1103.5665.

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Date of creation: Mar 2011
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Handle: RePEc:arx:papers:1103.5665

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  1. John Cotter & Kevin Dowd, 2011. "Extreme Spectral Risk Measures: An Application to Futures Clearinghouse Margin Requirements," Working Papers, Geary Institute, University College Dublin 200516, Geary Institute, University College Dublin.
  2. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1505-1518, July.
  3. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers, Centre de Recherche en Economie et Statistique 2000-05, Centre de Recherche en Economie et Statistique.
  4. O. Scaillet, 2004. "Nonparametric Estimation and Sensitivity Analysis of Expected Shortfall," Mathematical Finance, Wiley Blackwell, Wiley Blackwell, vol. 14(1), pages 115-129.
  5. Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
  6. Christian Gourieroux & Wei Liu, 2006. "Sensitivity Analysis of Distortion Risk Measures," Working Papers, Centre de Recherche en Economie et Statistique 2006-33, Centre de Recherche en Economie et Statistique.
  7. 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, Elsevier, vol. 7(3-4), pages 271-300, November.
  8. Matthew Pritsker, 1997. "Evaluating Value at Risk Methodologies: Accuracy versus Computational Time," Journal of Financial Services Research, Springer, Springer, vol. 12(2), pages 201-242, October.
  9. Tak Siu & Howell Tong & Hailiang Yang, 2004. "On Bayesian Value at Risk: From Linear to Non-Linear Portfolios," Asia-Pacific Financial Markets, Springer, Springer, vol. 11(2), pages 161-184, June.
  10. 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, Elsevier, vol. 26(7), pages 1317-1334, July.
  11. 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.
  12. Song Xi Chen, 2008. "Nonparametric Estimation of Expected Shortfall," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 6(1), pages 87-107, Winter.
  13. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers, Centre de Recherche en Economie et Statistique 2000-05, Centre de Recherche en Economie et Statistique.
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Cited by:
  1. Wächter, Hans Peter & Mazzoni, Thomas, 2013. "Consistent modeling of risk averse behavior with spectral risk measures," European Journal of Operational Research, Elsevier, Elsevier, vol. 229(2), pages 487-495.

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