CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles
AbstractValue 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 that 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. Utilizing the criterion from Regression Quantiles, and postulating a variety of dynamic updating processes we propose methods based on a Genetic Algorithm to estimate the unknown parameters of CAViaR models. We propose a Dynamic Quantile Test of model adequacy that tests the hypothesis that in each period the probability of exceeding the VaR must be independent of all the past information. 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.
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Bibliographic InfoPaper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0841.
Date of creation: 01 Aug 2000
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- Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
- Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
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