TY - JOUR AU - Engle,Robert F. AU - Manganelli,Simone TI - CAViaR: Conditional Value at Risk by Quantile Regression JF - National Bureau of Economic Research Working Paper Series VL - No. 7341 PY - 1999 Y2 - September 1999 UR - http://www.nber.org/papers/w7341 L1 - http://www.nber.org/papers/w7341.pdf N1 - Author contact info: Robert F. Engle, III Department of Finance, Stern School of Business New York University, Salomon Center 44 West 4th Street, Suite 9-160 New York, NY 10012-1126 Tel: 212/998-0710 Fax: 212/995-4220 E-Mail: rengle@stern.nyu.edu Simone Manganelli European Central Bank E-Mail: simone.manganelli@ecb.int AB - 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. ER -