An Extreme Value Approach to Estimating Volatility and Value at Risk*

Abstract

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.