CAViaR: Conditional Value at Risk by Quantile Regression
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 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.
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Bibliographic InfoPaper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 7341.
Date of creation: Sep 1999
Date of revision:
Publication status: published as 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.
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Find related papers by JEL classification:
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-1999-11-08 (All new papers)
- NEP-ECM-1999-11-08 (Econometrics)
- NEP-ETS-1999-11-08 (Econometric Time Series)
- NEP-FIN-1999-11-08 (Finance)
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- White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-61, January.
- repec:cup:etheor:v:7:y:1991:i:1:p:46-68 is not listed on IDEAS
- Powell, James L., 1984. "Least absolute deviations estimation for the censored regression model," Journal of Econometrics, Elsevier, vol. 25(3), pages 303-325, July.
- Engle, Robert F & Ng, Victor K, 1993.
" Measuring and Testing the Impact of News on Volatility,"
Journal of Finance,
American Finance Association, vol. 48(5), pages 1749-78, December.
- 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.
- Jon Danielsson & Casper G. de Vries, 1998.
"Beyond the Sample: Extreme Quantile and Probability Estimation,"
FMG Discussion Papers
dp298, Financial Markets Group.
- Jón Daníelsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," Tinbergen Institute Discussion Papers 98-016/2, Tinbergen Institute.
- Andrews, Donald W.K., 1988.
"Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables,"
Cambridge University Press, vol. 4(03), pages 458-467, December.
- Andrews, Donald W. K., 1987. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Working Papers 645, California Institute of Technology, Division of the Humanities and Social Sciences.
- White,Halbert, 1996.
"Estimation, Inference and Specification Analysis,"
Cambridge University Press, number 9780521574464, Fall.
- Powell, James L., 1986. "Censored regression quantiles," Journal of Econometrics, Elsevier, vol. 32(1), pages 143-155, June.
- Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(01), pages 46-68, March.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Granger, C. W. J. & White, Halbert & Kamstra, Mark, 1989. "Interval forecasting : An analysis based upon ARCH-quantile estimators," Journal of Econometrics, Elsevier, vol. 40(1), pages 87-96, January.
- 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, vol. 6(03), pages 295-317, September.
- repec:cup:etheor:v:6:y:1990:i:3:p:295-317 is not listed on IDEAS
- 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, vol. 39(4), pages 841-62, November.
- Rossi, Eduardo & Spazzini, Filippo, 2008.
"Model and distribution uncertainty in multivariate GARCH estimation: a Monte Carlo analysis,"
12260, University Library of Munich, Germany.
- Rossi, E. & Spazzini, F., 2010. "Model and distribution uncertainty in multivariate GARCH estimation: A Monte Carlo analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2786-2800, November.
- Eric Jondeau & Michael Rockinger, 2002. "Conditional Dependency of Financial Series: The Copula-GARCH Model," FAME Research Paper Series rp69, International Center for Financial Asset Management and Engineering.
- Engle, Robert F. & Manganelli, Simone, 2001. "Value at risk models in finance," Working Paper Series 0075, European Central Bank.
- Marco Bee & Fabrizio Miorelli, 2010. "Dynamic VaR models and the Peaks over Threshold method for market risk measurement: an empirical investigation during a financial crisis," Department of Economics Working Papers 1009, Department of Economics, University of Trento, Italia.
- Sandrine Lardic & Valérie Mignon, 2004. "Robert F. Engle et Clive W.J. Granger prix Nobel d'économie 2003," Revue d'économie politique, Dalloz, vol. 0(1), pages 1-15.
- J. David Cummins & David Lalonde & Richard D. Phillips, 2000.
"The Basis Risk of Catastrophic-Loss Index Securities,"
Center for Financial Institutions Working Papers
00-22, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Cummins, J. David & Lalonde, David & Phillips, Richard D., 2004. "The basis risk of catastrophic-loss index securities," Journal of Financial Economics, Elsevier, vol. 71(1), pages 77-111, January.
- Michelle L. Barnes & Anthony W. Hughes, 2002. "A quantile regression analysis of the cross section of stock market returns," Working Papers 02-2, Federal Reserve Bank of Boston.
- Kudryavtsev, Andrey A., 2009. "Using quantile regression for rate-making," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 296-304, October.
- Costello, Alexandra & Asem, Ebenezer & Gardner, Eldon, 2008. "Comparison of historically simulated VaR: Evidence from oil prices," Energy Economics, Elsevier, vol. 30(5), pages 2154-2166, September.
- Guidolin, Massimo & Timmermann, Allan, 2006.
"Term structure of risk under alternative econometric specifications,"
Journal of Econometrics,
Elsevier, vol. 131(1-2), pages 285-308.
- Guidolin, Massimo & Timmermann, Allan G, 2004. "Term Structure of Risk Under Alternative Econometric Specifications," CEPR Discussion Papers 4645, C.E.P.R. Discussion Papers.
- Massimo Guidolin & Allan Timmerman, 2005. "Term structure of risk under alternative econometric specifications," Working Papers 2005-001, Federal Reserve Bank of St. Louis.
- Bollerslev, Tim, 2001. "Financial econometrics: Past developments and future challenges," Journal of Econometrics, Elsevier, vol. 100(1), pages 41-51, January.
- Simone Manganelli & Lorenzo Cappiello & Bruno Gerard, 2004. "The Contagion Box: Measuring Co-Movements in Financial Markets by Regression Quantiles," Econometric Society 2004 Latin American Meetings 77, Econometric Society.
- Rockinger, M. & Jondeau, E., 2001.
"Conditional Dependency of Financial Series: An Application of Copulas,"
82, Banque de France.
- ROCKINGER, Michael & JONDEAU, Eric, 2001. "Conditional dependency of financial series : an application of copulas," Les Cahiers de Recherche 723, HEC Paris.
- Kritski, Oleg & Ulyanova, Marina, 2007. "Assessment of Multivariate Financial Risks of a Stock Share Portfolio," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 8(4), pages 3-17.
- Marcelo Bianconi & Joe A. Yoshino, 2012. "Worldwide Commodities Sector Market-To-Book and Return on Equity Valuation," Discussion Papers Series, Department of Economics, Tufts University 0772, Department of Economics, Tufts University.
- Ming-Yuan Leon Li & Hsiou-wei William Lin, 2004. "Estimating value-at-risk via Markov switching ARCH models - an empirical study on stock index returns," Applied Economics Letters, Taylor & Francis Journals, vol. 11(11), pages 679-691.
- Trino-Manuel Ñíguez, 2008. "Volatility and VaR forecasting in the Madrid Stock Exchange," Spanish Economic Review, Springer, vol. 10(3), pages 169-196, September.
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