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

Turan G. Bali ()
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Turan G. Bali: Department of Economics and Finance, Zicklin School of Business, Baruch College, City University of New York, One Bernard Baruch Way, Box 10-225, New York, New York 10010 and Department of Finance, College of Administrative Sciences and Economics, Koç University, Fener Yolu Caddesi, Sariyer 80910, Istanbul, Turkey

Management Science, 2007, vol. 53, issue 2, 323-339

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.

Keywords: extreme value distributions; interest-rate options; term structure of interest rates; volatility; skewed fat-tailed distributions (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:53:y:2007:i:2:p:323-339

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