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Empirical Issues in Value-at-Risk*

Published online by Cambridge University Press:  29 August 2014

Dennis Bams  and
Jacco L. Wielhouwer
Jacco L. Wielhouwer
Affiliation:
ING Bank, PO Box 1800, 1000 BV Amsterdam – The Netherlands, Telephone: + 31 20 576 1442, Fax: +31 20 576 1473, Email:Jacco.Wielhouwer@mail.ing.nl, J.L. Wielhouwer@kub.nl
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Abstract

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For the purpose of Value-at-Risk (VaR) analysis, a model for the return distribution is important because it describes the potential behavior of a financial security in the future. What is primarily, is the behavior in the tail of the distribution since VaR analysis deals with extreme market situations. We analyze the extension of the normal distribution function to allow for fatter tails and for time-varying volatility. Equally important to the distribution function are the associated parameter values. We argue that parameter uncertainty leads to uncertainty in the reported VaR estimates. There is a tradeoff between more complex tail-behavior and this uncertainty. The “best estimate”-VaR should be adjusted to take account of the uncertainty in the VaR. Finally, we consider the VaR forecast for a portfolio of securities. We propose a method to treat the modeling in a univariate, rather than a multivariate, framework. Such a choice allows us to reduce parameter uncertainty and to model directly the relevant variable.

Keywords

Value-at-RiskParameter UncertaintyTime-varying volatilityFat tails
Type
Workshop
Information
ASTIN Bulletin: The Journal of the IAA , Volume 31 , Issue 2 , November 2001 , pp. 299 - 315
Copyright
Copyright © International Actuarial Association 2001

Footnotes

*

We thank Johan van der Ende, two anonymous referees and participants of the AFIR-2000 colloquium for useful comments on an earlier draft. The usual disclaimer applies.

References

Bollerslev, T., Engle, R.F. and Nelson, D. (1994) ARCH Models, in Engle, R.F. and McFadden, D., eds, Handbook of Econometrics, volume IV, North Holland.Google Scholar
Drudi, F., Generale, A. and Majnoni, G. (1997) “Sensitivity of VaR measures to different risk methods”, Temi di Discussione, 317, Banca D'Italia. Available upon request from Banca D'ltalia, www.bancaditalia.itGoogle Scholar
Embrechts, P., Kluppelberg, C. and Mikosch, T. (1997) Modelling Extreme Events for Insurance and Finance, Springer Verlag, Berlin.CrossRefGoogle Scholar
Jorion, P. (1996) “Risk: Measuring the risk in Value at Risk”, Financial Analysts Journal, 52, 6, 47–56.CrossRefGoogle Scholar
Jorion, P. (2000) Value at Risk: The New Benchmark for Managing Financial Risk, McGraw-Hill, New York.Google Scholar
JP Morgan Bank (1996) Risk Metrics Technical Document, New York: JP Morgan Bank. Available from: www.riskmetrics.co.jpGoogle Scholar
Lucas, A. and Klaassen, P. (1998) “Extreme returns, downside risk and optimal asset allocation”, Journal of Portfolio Management, 25, 71–79.CrossRefGoogle Scholar
McNeil, A.J. and Frey, R. (2000) “Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach”, Journal of Empirical Finance, 7, 3–4, 271–300.CrossRefGoogle Scholar
Van den Goorbergh, R.W.J. and Vlaar, P.J.G. (1999) “Value at Risk Analysis of stock returns: Historical simulation, variance technique or tail index estimation?”, research memorandum WO&E, 579, De Nederlandsche Bank. Available via: http://www.gloriamundi.org/var/wps.html from www.dnb.nl/publicaties/pdf/staff40.pdfGoogle Scholar