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Extreme Value Theory and Value at Risk

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  • Viviana Fernández

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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 for some return series key to the Chilean financial market 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.dii.uchile.cl/~cea/sitedev/cea/www/download.php?file=documentos_trabajo/ASOCFILE120030327114904.pdf
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Bibliographic Info

Paper provided by Centro de Economía Aplicada, Universidad de Chile in its series Documentos de Trabajo with number 154.

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Date of creation: 2003
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Handle: RePEc:edj:ceauch:154

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Web page: http://www.dii.uchile.cl/cea/
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  1. 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.
  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.
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Cited by:
  1. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
  2. 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.
  3. L. Kourouma & D. Dupre & G. Sanfilippo & O. Taramasco, 2011. "Extreme Value at Risk and Expected Shortfall during Financial Crisis," Post-Print halshs-00658495, HAL.
  4. Rossignolo, Adrian F. & Fethi, Meryem Duygun & Shaban, Mohamed, 2012. "Value-at-Risk models and Basel capital charges," Journal of Financial Stability, Elsevier, vol. 8(4), pages 303-319.

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