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Extreme Value Theory and Value at Risk

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Author Info
Viviana Fernandez () (University of Chile)

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Abstract

Value at Risk (VaR) is a measure of the maximum potential change in value of a portfolio of financial assets with a given probability over a given time horizon. VaR became a key measure of market risk since the Basle Committee stated that banks should be able to cover losses on their trading portfolios over a ten-day horizon, 99 percent of the time. A common practice is to compute VaR by assuming that changes in value of the portfolio are normally distributed, conditional on past information. However, assets returns usually come from fat-tailed distributions. Therefore, computing VaR under the assumption of conditional normality can be an important source of error. We illustrate this point with Chilean and U.S. returns series by resorting to extreme value theory (EVT) and GARCH-type models. In addition, we show that dynamic estimation of empirical quantiles can also give more accurate VaR estimates than quantiles of a standard normal.

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File URL: http://www.economia.uahurtado.cl/pdf/publicaciones/Fernandez2003.pdf
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Publisher Info
Article provided by Ilades-Georgetown University, Economics Department in its journal Revista de Analisis Economico.

Volume (Year): 18 (2003)
Issue (Month): 1 (June)
Pages: 57-85
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Handle: RePEc:ila:anaeco:v:18:y:2003:i:1:p:57-85

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Related research
Keywords: risk; VAR; GARCH;

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Find related papers by JEL classification:
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Christian A. Johnson, 2002. "Value at Risk: Teoría y Aplicaciones," Working Papers Central Bank of Chile 136, Central Bank of Chile. [Downloadable!]
  2. Robert Engle, 2001. "GARCH 101: The Use of ARCH/GARCH Models in Applied Econometrics," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 157-168, Fall. [Downloadable!] (restricted)
  3. 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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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Gonzalo Cortazar & Alejandro Bernales & Diether Beuermann, 2005. "Methodology and Implementation of Value-at-Risk Measures in Emerging Fixed-Income Markets with Infrequent Trading," Finance 0512030, EconWPA. [Downloadable!]
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