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The Extreme Value Theory and Copulas as a Tool to Measure Market Risk

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  • Krenar Avdulaj

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Abstract

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 gives higher estimates of VaR for extreme events, while variance-covariance lower. The method that we illustrate gives a result in between the two 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, 2012. "The Extreme Value Theory and Copulas as a Tool to Measure Market Risk," Bulletin of the Czech Econometric Society, The Czech Econometric Society, vol. 19(29).
  • Handle: RePEc:czx:journl:v:19:y:2012:i:29:id:192
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    File URL: http://ces.utia.cas.cz/bulletin/index.php/bulletin/article/view/192
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    Keywords

    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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