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CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles

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  • Robert Engle

    (University of California)

  • Simone Manganelli

    (University of California)

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 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 Info

Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 0841.

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Date of creation: 01 Aug 2000
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Handle: RePEc:ecm:wc2000:0841

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  1. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 7(01), pages 46-68, March.
  2. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-62, November.
  3. repec:cup:etheor:v:6:y:1990:i:3:p:295-317 is not listed on IDEAS
  4. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  5. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 4(03), pages 458-467, December.
  6. repec:cup:etheor:v:7:y:1991:i:1:p:46-68 is not listed on IDEAS
  7. Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, Elsevier, vol. 40(1), pages 87-96, January.
  8. Foresi, S. & Paracchi, F., 1992. "The Conditional Distribution of Excess Returns: An Empirical Analysis," Working Papers, C.V. Starr Center for Applied Economics, New York University 92-49, C.V. Starr Center for Applied Economics, New York University.
  9. repec:wop:humbsf:1998-36 is not listed on IDEAS
  10. Jon Danielsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," FMG Discussion Papers, Financial Markets Group dp298, Financial Markets Group.
  11. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 6(03), pages 295-317, September.
  12. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, Econometric Society, vol. 52(1), pages 143-61, January.
  13. Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, Elsevier, vol. 25(3), pages 303-325, July.
  14. Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, Elsevier, vol. 32(1), pages 143-155, June.
  15. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 33-50, January.
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