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

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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)

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.

Suggested Citation

  • Turan G. Bali, 2007. "An Extreme Value Approach to Estimating Interest-Rate Volatility: Pricing Implications for Interest-Rate Options," Management Science, INFORMS, vol. 53(2), pages 323-339, February.
    • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:2:p:323-339
    DOI: 10.1287/mnsc.1060.0628
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    2. Switzer, Lorne N. & Tahaoglu, Cagdas & Zhao, Yun, 2017. "Volatility measures as predictors of extreme returns," Review of Financial Economics, Elsevier, vol. 35(C), pages 1-10.
    3. So, Mike K.P. & Chan, Raymond K.S., 2014. "Bayesian analysis of tail asymmetry based on a threshold extreme value model," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 568-587.
    4. Ji, Jingru & Wang, Donghua & Xu, Dinghai & Xu, Chi, 2020. "Combining a self-exciting point process with the truncated generalized Pareto distribution: An extreme risk analysis under price limits," Journal of Empirical Finance, Elsevier, vol. 57(C), pages 52-70.
    5. Yalcin Akcay & Atakan Yalcin, 2010. "Optimal Portfolio Selection With A Shortfall Probability Constraint: Evidence From Alternative Distribution Functions," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 33(1), pages 77-102, March.
    6. Fanelli, Viviana, 2017. "Implications of implicit credit spread volatilities on interest rate modelling," European Journal of Operational Research, Elsevier, vol. 263(2), pages 707-718.
    7. Hainaut, Donatien, 2016. "A bivariate Hawkes process for interest rate modeling," Economic Modelling, Elsevier, vol. 57(C), pages 180-196.
    8. Ibrahim Ergen, 2015. "Two-step methods in VaR prediction and the importance of fat tails," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1013-1030, June.

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