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Extreme Value Theory and Value at Risk

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  • Viviana Fernandez

    () (University of Chile)

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.

Suggested Citation

  • Viviana Fernandez, 2003. "Extreme Value Theory and Value at Risk," Revista de Analisis Economico – Economic Analysis Review, Ilades-Georgetown University, Universidad Alberto Hurtado/School of Economics and Bussines, vol. 18(1), pages 57-85, June.
    • Handle: RePEc:ila:anaeco:v:18:y:2003:i:1:p:57-85
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    References listed on IDEAS

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    1. 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.
    2. Engle, Robert F & Gonzalez-Rivera, Gloria, 1991. "Semiparametric ARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(4), pages 345-359, October.
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    Cited by:

    1. Nguyen, Cuong C. & Bhatti, M. Ishaq, 2012. "Copula model dependency between oil prices and stock markets: Evidence from China and Vietnam," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 22(4), pages 758-773.
    2. 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.
    3. Nikola Radivojevic & Milena Cvjetkovic & Saša Stepanov, 2016. "The new hybrid value at risk approach based on the extreme value theory," Estudios de Economia, University of Chile, Department of Economics, vol. 43(1 Year 20), pages 29-52, June.
    4. L. Kourouma & D. Dupre & G. Sanfilippo & O. Taramasco, 2011. "Extreme Value at Risk and Expected Shortfall during Financial Crisis," Post-Print halshs-00658495, HAL.
    5. 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.
    6. 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, University Library of Munich, Germany.
    7. de Jesús, Raúl & Ortiz, Edgar & Cabello, Alejandra, 2013. "Long run peso/dollar exchange rates and extreme value behavior: Value at Risk modeling," The North American Journal of Economics and Finance, Elsevier, vol. 24(C), pages 139-152.

    More about this item

    Keywords

    risk; VAR; GARCH;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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