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Value at risk models in finance

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Author Info
Simone Manganelli () (European Central Bank, Kaiserstrasse 29, Postfach 16 03 19, 60066 Frankfurt am Main, Germany.)
Robert F. Engle (New York University - Department of Economics, 269 Mercer Street, New York , NY 10003, United States.)

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Abstract

The main objective of this paper is to survey and evaluate the performance of the most popular univariate VaR methodologies, paying particular attention to their underlying assumptions and to their logical flaws. In the process, we show that the Historical Simulation method and its variants can be considered as special cases of the CAViaR framework developed by Engle and Manganelli (1999). We also provide two original methodological contributions. The first one introduces the extreme value theory into the CAViaR model. The second one concerns the estimation of the expected shortfall (the expected loss, given that the return exceeded the VaR) using a regression technique. The performance of the models surveyed in the paper is evaluated using a Monte Carlo simulation. We generate data using GARCH processes with different distributions and compare the estimated quantiles to the true ones. The results show that CAViaR models perform best with heavy-tailed DGP. JEL Classification: C22; G22.

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Paper provided by European Central Bank in its series Working Paper Series with number 075.

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Length: 41 pages
Date of creation: Aug 2001
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Handle: RePEc:ecb:ecbwps:20010075

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Related research
Keywords: Value at risk; CAViaR; extreme value theory.;

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References listed on IDEAS
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  1. Francis X. Diebold & Til Schuermann & John D. Stroughair, 1998. "Pitfalls and Opportunities in the Use of Extreme Value Theory in Risk Management," New York University, Leonard N. Stern School Finance Department Working Paper Seires 98-081, New York University, Leonard N. Stern School of Business-.
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  2. C. Gouriéroux & J. Jasiak, . "Truncated Maximum Likelihood, Goodness of Fit Tests and Tail Analysis," Sonderforschungsbereich 373 1998-36, Humboldt Universitaet Berlin.
  3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  4. Robert F. Engle & Simone Manganelli, 1999. "CAViaR: Conditional Value at Risk by Quantile Regression," NBER Working Papers 7341, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Jón Daníelsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," Tinbergen Institute Discussion Papers 98-016/2, Tinbergen Institute. [Downloadable!]
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  6. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. Vries, Caspar de & Danielsson, Jon, 1996. "Tail Index and Quantile Estimation with Very High Frequency Data," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich.
  8. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-59, October.
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  9. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November. [Downloadable!] (restricted)
  10. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July. [Downloadable!] (restricted)
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  1. Maria Rosa Nieto & Esther Ruiz, 2008. "Measuring financial risk : comparison of alternative procedures to estimate VaR and ES," Statistics and Econometrics Working Papers ws087326, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  2. Gonzales-Martínez, Rolando, 2009. "La Gestión de Riesgo de Liquidez en Economías Emergentes: Un Modelo Valor-en-Riesgo (VaR) Paramétrico de Calibración Indirecta y una Aplicación al Sistema Financiero Boliviano
    [Liquidity Risk     ," MPRA Paper 14247, University Library of Munich, Germany. [Downloadable!]
  3. George Kouretas & Leonidas Zarangas, 2005. "Conditional autoregressive valu at risk by regression quantile: Estimatingmarket risk for major stock markets," Working Papers 0521, University of Crete, Department of Economics. [Downloadable!]
  4. Christian A. Johnson, 2002. "Value at Risk: Teoría y Aplicaciones," Working Papers Central Bank of Chile 136, Central Bank of Chile. [Downloadable!]
  5. Lima, Luiz Renato Regis de Oliveira & Neri, Breno de Andrade Pinheiro, 2006. "Comparing Value-at-Risk Methodologies," Economics Working Papers (Ensaios Economicos da EPGE) 629, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
    Other versions:
  6. 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. [Downloadable!]
  7. Panayiotis Diamandis & Georgios Kouretas & Leonidas Zarangas, 2006. "Value-at-Risk for long and short trading positions: The case of the Athens Stock Exchange," Working Papers 0601, University of Crete, Department of Economics. [Downloadable!]
  8. Karoll Gómez Portilla & Santiago Gallón Gómez, 2007. "Distribución condicional de los retornos de la tasa de cambio colombiana: un ejercicio empírico a partir de modelos GARCH multivariados," REVISTA DE ECONOMÍA DEL ROSARIO, UNIVERSIDAD DEL ROSARIO - FACULTAD DE ECONOMÍA. [Downloadable!]
  9. Massimo Guidolin & Allan Timmerman, 2005. "Term structure of risk under alternative econometric specifications," Working Papers 2005-001, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  10. Marco Filagrana, 2002. "Il model risk nella gestione dei rischi di mercato," Alea Tech Reports 015, Department of Computer and Management Sciences, University of Trento, Italy, revised 14 Jun 2008. [Downloadable!]
  11. Quan Gan & Robert J. Hill, 2008. "Measuring Housing Affordability: Looking Beyond the Median," Discussion Papers 2008-09, School of Economics, The University of New South Wales. [Downloadable!]
    Other versions:
  12. Enrico Zaninotto & Alessandro Rossi & Loris Gaio, 1999. "Stochastic learning in coordination games: a simulation approach," Quaderni DISA 015, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jun 2003. [Downloadable!]
    Other versions:
  13. Wolfgang Aussenegg & Tatiana Miazhynskaia, 2006. "Uncertainty in Value-at-risk Estimates under Parametric and Non-parametric Modeling," Financial Markets and Portfolio Management, Springer, vol. 20(3), pages 243-264, September. [Downloadable!] (restricted)
  14. Giannis Vardas & Anastasios Xepapadeas, 2006. "Preserving Biodiversity: Ambiguity and Safety Rules," Working Papers 0607, University of Crete, Department of Economics. [Downloadable!]
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