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Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities

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  • Robert R. Bliss
  • Ehud I. Ronn
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    Abstract

    Previous studies on interest rate derivatives have been limited by the relatively short history of most traded derivative securities. The prices for callable U.S. Treasury securities, available for the period 1926–95, provide the sole source of evidence concerning the implied volatility of interest rates over this extended period. Using the prices of callable, as well as non-callable, Treasury instruments, this paper estimates implied interest rate volatilities for the past seventy years. Our technique for estimating implied volatilities enables us to address two important issues concerning callable bonds: the apparent presence of negative embedded option values and the optimal policy for calling these, and similarly structured, deferred-exercise embedded option bonds. ; In examining the issue of negative option value callable bonds, our technique enables us to extend significantly both the sample period and sample breadth beyond those covered by other investigators of this phenomenon and to resolve the inconsistencies in their results. We show that the frequency of mispriced bonds is time-varying and that there also exist irrationally underpriced bonds. Critically, both anomalies are shown to be related to volatility-insensitive, away-from-the-money bonds. ; In contrast to the naive call decision rules suggested by previous authors, we develop the option-theoretic optimal call policy for deferred-exercised "Bermuda"-style options for which prior notification of intent to call is required. We do this by introducing the concept of "threshold volatility" to measure the point at which the time value of the embedded call option has been eroded to zero. By using this concept, we address the valuation of such bonds and document the frequent optimality of the Treasury's past call decisions for U.S. government obligations.

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    Bibliographic Info

    Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 97-1.

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    Date of creation: 1997
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    Publication status: Published in Journal of Business, April 1998
    Handle: RePEc:fip:fedawp:97-1

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    Keywords: Derivative securities ; Government securities;

    References

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    1. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
    2. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
    3. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 419-440, December.
    4. Fama, Eugene F & Bliss, Robert R, 1987. "The Information in Long-Maturity Forward Rates," American Economic Review, American Economic Association, vol. 77(4), pages 680-92, September.
    5. Charles R. Nelson & Andrew F. Siegel, 1986. "Long-Term Behavior of Yield Curves," NBER Working Papers 1789, National Bureau of Economic Research, Inc.
    6. Robert R. Bliss, 1996. "Testing term structure estimation methods," Working Paper 96-12, Federal Reserve Bank of Atlanta.
    7. Ronn, Ehud I., 1987. "A New Linear Programming Approach to Bond Portfolio Management," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 439-466, December.
    8. Jordan, Bradford D. & Jordan, Susan D., 1991. "Tax options and the pricing of treasury bond triplets : Theory and evidence," Journal of Financial Economics, Elsevier, vol. 30(1), pages 135-164, November.
    9. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
    10. Livingston, Miles B & Jain, Suresh K, 1982. " Flattening of Bond Yield Curves for Long Maturities," Journal of Finance, American Finance Association, vol. 37(1), pages 157-67, March.
    11. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
    12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    13. Schaefer, Stephen M., 1982. "Tax-induced clientele effects in the market for British government securities : Placing bounds on security values in an incomplete market," Journal of Financial Economics, Elsevier, vol. 10(2), pages 121-159, July.
    14. Vu, Joseph D., 1986. "An empirical investigation of calls of non-convertible bonds," Journal of Financial Economics, Elsevier, vol. 16(2), pages 235-265, June.
    15. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
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