An Extreme Value Approach to Estimating Interest-Rate Volatility: Pricing Implications for Interest-Rate Options

Abstract

This paper proposes an extreme value approach to estimating interest-rate volatility, and shows that during the extreme movements of the U.S. Treasury market the volatility of interest-rate changes is underestimated by the standard approach that uses the thin-tailed normal distribution. The empirical results indicate that (1) 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; (2) the minimal changes are more volatile than the maximal changes for all data sets and for all asymptotic distributions used; (3) the minimal changes in Treasury yields have fatter tails than the maximal changes; and (4) for both the maxima and minima, the extreme changes in short-term rates have thicker tails than the extreme changes in long-term rates. This paper extends the standard option-pricing models with lognormal forward rates to accommodate significant kurtosis observed in the interest-rate data. This paper introduces a closed-form option-pricing model based on the generalized extreme value distribution that successfully removes the well-known pricing bias of the lognormal distribution.