Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities
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.
|Date of creation:||1997|
|Date of revision:|
|Publication status:||Published in Journal of Business, April 1998|
|Contact details of provider:|| Postal: 1000 Peachtree St., N.E., Atlanta, Georgia 30309|
Web page: http://www.frbatlanta.org/
More information through EDIRC
|Order Information:|| Email: |
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- 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.
- 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.
- 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.
- Charles R. Nelson & Andrew F. Siegel, 1986.
"Long-Term Behavior of Yield Curves,"
NBER Working Papers
1789, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Tom Doan, . "RATS programs to replicate CKLS(1992) estimation of interest rate models," Statistical Software Components RTZ00035, Boston College Department of Economics.
- 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.
- 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.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- 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.
- 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.
- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
- 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.
- Robert R. Bliss, 1996. "Testing term structure estimation methods," FRB Atlanta Working Paper 96-12, Federal Reserve Bank of Atlanta.
When requesting a correction, please mention this item's handle: RePEc:fip:fedawp:97-1. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Elaine Clokey)
If references are entirely missing, you can add them using this form.