Value at risk models in finance
The main objective of this paper is to survey and evaluate the performance of the most popular univariate VaR methodologies, paying particular attention to their underlying assumptions and to their logical flaws. In the process, we show that the Historical Simulation method and its variants can be considered as special cases of the CAViaR framework developed by Engle and Manganelli (1999). We also provide two original methodological contributions. The first one introduces the extreme value theory into the CAViaR model. The second one concerns the estimation of the expected shortfall (the expected loss, given that the return exceeded the VaR) using a regression technique. The performance of the models surveyed in the paper is evaluated using a Monte Carlo simulation. We generate data using GARCH processes with different distributions and compare the estimated quantiles to the true ones. The results show that CAViaR models perform best with heavy-tailed DGP. JEL Classification: C22, G22
|Date of creation:||Aug 2001|
|Contact details of provider:|| Postal: 60640 Frankfurt am Main, Germany|
Phone: +49 69 1344 0
Fax: +49 69 1344 6000
Web page: http://www.ecb.europa.eu/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
- Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998.
"Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management,"
New York University, Leonard N. Stern School Finance Department Working Paper Seires
98-081, New York University, Leonard N. Stern School of Business-.
- Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," Center for Financial Institutions Working Papers 98-10, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(03), pages 295-317, September.
- 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.
- Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc.
- Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
- Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
- Benoit Mandelbrot, 1963.
"The Variation of Certain Speculative Prices,"
The Journal of Business,
University of Chicago Press, vol. 36, pages 1-394.
- Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
- Jón Daníelsson & Casper G. de Vries, 1998.
"Beyond the Sample: Extreme Quantile and Probability Estimation,"
Tinbergen Institute Discussion Papers
98-016/2, Tinbergen Institute.
- Jon Danielsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," FMG Discussion Papers dp298, Financial Markets Group.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
When requesting a correction, please mention this item's handle: RePEc:ecb:ecbwps:20010075. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Official Publications)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.