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An Extreme Value Approach to Estimating Volatility and Value at Risk


  • Turan G. Bali

    (Baruch College)


This article determines the type of asymptotic distribution for the extreme changes in U.S. Treasury yields. The thin-tailed Gumbel and exponential distributions are strongly rejected against the fat-tailed Frechet and Pareto distributions. The empirical results indicate that the volatility of maximal and minimal changes in interest rates declines as time-to-maturity rises, yielding a downward-sloping volatility curve for the extremes. The article proposes an extreme value approach to estimating value at risk and shows that the statistical theory of extremes provides a more accurate approach for risk management and value at risk (VaR) calculations than the standard models.

Suggested Citation

  • Turan G. Bali, 2003. "An Extreme Value Approach to Estimating Volatility and Value at Risk," The Journal of Business, University of Chicago Press, vol. 76(1), pages 83-108, January.
  • Handle: RePEc:ucp:jnlbus:v:76:y:2003:i:1:p:83-108

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