Heterogeneous-Expectations Model of the Value of Bonds Bearing Call Options

Abstract

This paper develops a dynamic programming model of the optimal refunding strategy and the corresponding value of a callable bond. The model differs from previous work on this subject primarily in that it explicitly admits the possibility of differences between the issuer's expectations of future interest rates and an investor's corresponding expectations. This generalization facilitates the application of the model to determine what a specific bond (issued, for example, by a particular corporation) is worth to any given investor. Additional analytical features of the model, which differ from corresponding aspects of some previous models, include the use of a stochastic discounting rate and the use of continuous distributions to characterize the relevant interest rate expectations. For the bond issuer, his own expectations (together with the bond's coupon and call features) suffice to indicate the critical refunding yield as well as the expected value of the bond in each time period until the bond matures. For an investor, however, the analytical solution of the model and the illustrative numerical examples presented in the paper show that the issuer's expectations and the investor's own both matter if the two differ.