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Value at Risk Models in Finance

41 Pages Posted: 25 Feb 2003  

Simone Manganelli

European Central Bank (ECB)

Robert F. Engle

New York University - Leonard N. Stern School of Business - Department of Economics; New York University (NYU) - Department of Finance; National Bureau of Economic Research (NBER)

Date Written: August 2001

Abstract

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.

Keywords: Value at Risk; CAViaR; Extreme Value Theory

JEL Classification: C22, G22

Suggested Citation

Manganelli , Simone and Engle, Robert F., Value at Risk Models in Finance (August 2001). ECB Working Paper No. 75. Available at SSRN: https://ssrn.com/abstract=356220

Simone Manganelli (Contact Author)

European Central Bank (ECB) ( email )

Kaiserstrasse 29
Frankfurt am Main, 60311
Germany

HOME PAGE: http://www.simonemanganelli.org

Robert Engle

New York University - Leonard N. Stern School of Business - Department of Economics ( email )

269 Mercer Street
New York, NY 10003
United States

New York University (NYU) - Department of Finance

Stern School of Business
44 West 4th Street
New York, NY 10012-1126
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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