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The Extreme Value Theory as a Tool to Measure Market Risk



Assessing the extreme events is crucial in financial risk management. All risk managers and financial institutions want to know the risk of their portfolio under rare events scenarios. We illustrate a multivariate market risk estimating method which employs Monte Carlo simulations to estimate Value-at-Risk (VaR) for a portfolio of 4 stock exchange indexes from Central Europe. The method uses the non-parametric empirical distribution to capture small risks and the parametric Extreme Value theory to capture large and rare risks. We compare estimates of this method with historical simulation and variance-covariance method under low and high volatility samples of data. In general historical simulation method overestimates the VaR for extreme events, while variance-covariance underestimates it. The method that we illustrate gives a result in between because it considers historical performance of the stocks and also corrects for the heavy tails of the distribution. We conclude that the estimate method that we illustrate here is useful in estimating VaR for extreme events, especially for high volatility times.

Suggested Citation

  • Krenar Avdulaj, 2011. "The Extreme Value Theory as a Tool to Measure Market Risk," Working Papers IES 2011/26, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2011.
  • Handle: RePEc:fau:wpaper:wp2011_26

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    References listed on IDEAS

    1. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
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    Cited by:

    1. David E. Giles & Qinlu Chen, 2014. "Risk Analysis for Three Precious Metals: An Application of Extreme Value Theory," Econometrics Working Papers 1402, Department of Economics, University of Victoria.

    More about this item


    Value-at-Risk; Extreme Value Theory; copula.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

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