Caviar: Conditional Value at Risk by Quantile Regression

54 Pages Posted: 17 Feb 2000 Last revised: 13 Oct 2010

See all articles by Simone Manganelli

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: September 1999

Abstract

Value at Risk has become the standard measure of market risk employed by financial institutions for both internal and regulatory purposes. Despite its conceptual simplicity, its measurement is a very challenging statistical problem and none of the methodologies developed so far give satisfactory solutions. Interpreting Value at Risk as a quantile of future portfolio values conditional on current information, we propose a new approach to quantile estimation which does not require any of the extreme assumptions invoked by existing methodologies (such as normality or i.i.d. returns). The Conditional Value at Risk or CAViaR model moves the focus of attention from the distribution of returns directly to the behavior of the quantile. We postulate a variety of dynamic processes for updating the quantile and use regression quantile estimation to determine the parameters of the updating process. Tests of model adequacy utilize the criterion that each period the probability of exceeding the VaR must be independent of all the past information. We use a differential evolutionary genetic algorithm to optimize an objective function which is non-differentiable and hence cannot be optimized using traditional algorithms. Applications to simulated and real data provide empirical support to our methodology and illustrate the ability of these algorithms to adapt to new risk environments.

Suggested Citation

Manganelli, Simone and Engle, Robert F., Caviar: Conditional Value at Risk by Quantile Regression (September 1999). NBER Working Paper No. w7341. Available at SSRN: https://ssrn.com/abstract=195948

Simone Manganelli

European Central Bank (ECB) ( email )

Kaiserstrasse 29
Frankfurt am Main, 60311
Germany

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

Robert F. Engle (Contact Author)

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)

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Cambridge, MA 02138
United States

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