02475cam a22002537 4500001000600000003000500006005001700011008004100028100002100069245012400090260006600214490004100280500002000321520139700341530006101738538007201799538003601871690009901907700002402006710004202030830007602072856003702148856003602185w7341NBER20160724150311.0160724s1999 mau||||fs|||| 000 0 eng d1 aEngle, Robert F.10aCAViaRh[electronic resource]:bConditional Value at Risk by Quantile Regression /cRobert F. Engle, Simone Manganelli. aCambridge, Mass.bNational Bureau of Economic Researchc1999.1 aNBER working paper seriesvno. w7341 aSeptember 1999.3 aValue 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. aHardcopy version available to institutional subscribers. aSystem requirements: Adobe [Acrobat] Reader required for PDF files. aMode of access: World Wide Web. 7aC14 - Semiparametric and Nonparametric Methods: General2Journal of Economic Literature class.1 aManganelli, Simone.2 aNational Bureau of Economic Research. 0aWorking Paper Series (National Bureau of Economic Research)vno. w7341.4 uhttp://www.nber.org/papers/w734141uhttp://dx.doi.org/10.3386/w7341