Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T06:42:48.584Z Has data issue: false hasContentIssue false
  • English
  • Français

Quantifying and Correcting the Bias in Estimated Risk Measures

Published online by Cambridge University Press:  17 April 2015

Joseph Hyun Tae Kim  and
Mary R. Hardy
Joseph Hyun Tae Kim
Affiliation:
Statistics and Actuarial Science, University of Waterloo, Waterloo, ON, Canada
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we explore the bias in the estimation of the Value at Risk and Conditional Tail Expectation risk measures using Monte Carlo simulation. We assess the use of bootstrap techniques to correct the bias for a number of different examples. In the case of the Conditional Tail Expectation, we show that application of the exact bootstrap can improve estimates, and we develop a practical guideline for assessing when to use the exact bootstrap.

Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 365 - 386
Copyright
Copyright © ASTIN Bulletin 2007

Footnotes

*

Joseph Kim acknowledges the support in part of the Ph.D. Grant of the Society of Actuaries and the PGS-D2 grant of the Natural Sciences and Engineering Research Council of Canada.

§

Mary Hardy acknowledges the support of the Natural Sciences and Engineering Research Council of Canada.

References

AAA Life Capital Adequacy Subcommittee (2005) Recommended approach for setting regulatory risk-based capital requirements for variable annuities and similar products. Report, American Academy of Actuaries, Boston, MA.Google Scholar
Artzner, P., Delbaen, F., Eber, J.M. and Heath, D. (1999) Coherent measure of risk. Mathematical Finance, 203–228.CrossRefGoogle Scholar
CIA Segregated Funds Task Force (2002) Report of the CIA task force on segregated fund investment guarantees. Technical report, Canadian Institute of Actuaries, Ottawa, ON.Google Scholar
David, H.A. (1981) Order statistics. John Wiley & Sons, New York, 2nd edition.Google Scholar
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap methods and their application. Cambridge University Press, New York.CrossRefGoogle Scholar
Efron, B. and Tibshirani, R.J. (1993) An introduction to the bootstrap. Chapman & Hall, New York.CrossRefGoogle Scholar
Hall, P. (1992) The Bootstap and Edgeworth Expansion. Springer Series in Statistics. Springer-Verlag, New York.CrossRefGoogle Scholar
Hardy, M.R. (2003) Investment Guarantees: Modeling and Risk Management for Equity-Linked Life Insurance. John Wiley & Sons, New York.Google Scholar
Harrell, F.E. and Davis, C.E. (1982) A new distribution-free quantile estimator. Biometrika, 69(3), 635–640.CrossRefGoogle Scholar
Hutson, A.D. and Ernst, M.D. (2000) The exact bootstrap mean and variance of an L-estimator. Journal of Royal Statistical Society: Series B, 62, 89–94.CrossRefGoogle Scholar
Hyndman, R.J. and Fan, Y. (1996) Sample quantiles in statistical packages. The American Statistician, 50(4), 361–365.Google Scholar
Inui, K., Kijima, M. and Kitano, A. (2005) VaR is subject to a significant positive bias. Statistics & Probability Letters, 72, 299–311.CrossRefGoogle Scholar
Jeske, D.R. and Sampath, A. (2003) A real example that illustrates interesting properties of boostrap bias correction. The American Statistician, 57(1), 62–65.CrossRefGoogle Scholar
Johnson, N.L., Kotz, S. and Kemp, A.W. (1992) Univariate Discrete Distribution. John Wiley & Sons, New York, 2nd edition.Google Scholar
Klugman, S., Panjer, H. and Willmot, G. (1998) Loss Models. John Wiley, New York.Google Scholar
Manistre, B.J. and Hancock, G.H. (2005) Variance of the CTE estimator. North American Actuarial Journal, 9(2), 129–156.CrossRefGoogle Scholar
Mausser, H. (2001) Calculating quantile-based risk analytics with L-estimators. Algo Research Quarterly, 4(4), 33–47.Google Scholar
Rychlik, T. (1998) Bounds for expectations of L-estimates. In Balakrishnan, N. and Rao, C.R., editors, Handbook of Statistics, volume 16, Amsterdam. Elsevier.Google Scholar
Wirch, J.L. and Hardy, M.R. (1999) A synthesis of risk measures for capital adequacy. Insurance: Mathematics and Economics, 25, 337–347.Google Scholar