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Interest Rate Uncertainty and the Value of Bond Call Protection


  • Bodie, Zvi
  • Friedman, Benjamin Morton


This paper uses a model of the valuation of bonds bearing call options, together with observed market yields on callable bonds, to infer information about the uncertainty associated with interest rate expectations. A dynamic programming solution of the model simultaneously determines both the bond price and the issuer's optimal refunding strategy, given the relevant data describing the bond and the market's expectations of future interest rates. Application of the valuation model in reverse, for quarterly average data for 1969-76, generates a time series representing the uncertainty which the market associated with its expectations of future interest rates during this interval, given the then-prevailing yields on new issues of utility bonds and industrial bonds callable after 5 years and 10 years, respectively. This uncertainty, parameterized as the standard deviation of a truncated normal distribution, fluctuated between 1/2 percent and 3/4 percent between 1969 and early 1974, then rose to sharply higher levels from mid-1974 through mid-1975, and has fluctuated between 3/4 percent and 1 percent since late 1975.

Suggested Citation

  • Bodie, Zvi & Friedman, Benjamin Morton, 1978. "Interest Rate Uncertainty and the Value of Bond Call Protection," Scholarly Articles 4554310, Harvard University Department of Economics.
  • Handle: RePEc:hrv:faseco:4554310

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    References listed on IDEAS

    1. F. A. Lutz, 1940. "The Structure of Interest Rates," The Quarterly Journal of Economics, Oxford University Press, vol. 55(1), pages 36-63.
    2. Ofer, Aharon R & Taggart, Robert A, Jr, 1977. "Bond Refunding: A Clarifying Analysis," Journal of Finance, American Finance Association, vol. 32(1), pages 21-30, March.
    3. Elton, Edwin J & Gruber, Martin J, 1972. "The Economic Value of the Call Option," Journal of Finance, American Finance Association, vol. 27(4), pages 891-901, September.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. Modigliani, Franco & Shiller, Robert J, 1973. "Inflation, Rational Expectations and the Term Structure of Interest Rates," Economica, London School of Economics and Political Science, vol. 40(157), pages 12-43, February.
    6. Frank C. Jen & James E. Wert, 1967. "The Effect Of Call Risk On Corporate Bond Yields," Journal of Finance, American Finance Association, vol. 22(4), pages 637-651, December.
    7. Kraus, Alan, 1973. "The Bond Refunding Decision in an Efficient Market," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(05), pages 793-806, December.
    8. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    9. Fair, Ray C & Malkiel, Burton G, 1971. "The Determination of Yield Differentials between Debt Instruments of the Same Maturity," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 3(4), pages 733-749, November.
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    Cited by:

    1. Benjamin M. Friedman, 1981. "The Roles of Money and Credit in Macroeconomic Analysis," NBER Working Papers 0831, National Bureau of Economic Research, Inc.
    2. Benjamin M. Friedman, 1981. "Financing Capital Formation in the 1980s: Issues for Public Policy," NBER Working Papers 0745, National Bureau of Economic Research, Inc.
    3. Zvi Bodie & Benjamin M. Friedman, 1977. "Heterogeneous-Expectations Model of the Value of Bonds Bearing Call Options," NBER Working Papers 0218, National Bureau of Economic Research, Inc.
    4. Stephen A. Buser & Patric H. Hendershott, 1984. "The Pricing of Default-Free Mortgages," NBER Working Papers 1408, National Bureau of Economic Research, Inc.
    5. Benjamin M. Friedman, 1978. "Who Puts the Inflation Premium Into Nominal Interests Rates?," NBER Working Papers 0231, National Bureau of Economic Research, Inc.
    6. Clifford F. Thies, 1985. "New Estimates Of The Term Structure Of Interest Rates: 1920–1939," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 8(4), pages 297-306, December.
    7. Benjamin M. Friedman, 1982. "Federal Reserve Policy, Interest Rate Volatility, and the U.S. Capital Raising Mechanism," NBER Working Papers 0917, National Bureau of Economic Research, Inc.

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