On the application of the Black and Scholes formula to valuing bonds with embedded options: the case of extendible bonds

Abstract

This paper demonstrates how the Black and Scholes model can be applied to the valuation of a class of bonds with embedded options, namely, extendible bonds. The paper suggests an approach to estimate the model's parameters necessary for the valuation of the embedded options and the associated bonds. It then goes on to empirically price Canadian government extendible bonds and their embedded options for the period 1967 to 1987. The findings show that the Black and Scholes model overestimated the implied market call option to extend the life of the bond or that investors underpriced the option to extend, assuming that the estimated Black and Scholes call prices are correct. While, in dollar terms, the underpricing of the embedded options was more severe in 1980–87 than in 1967–79, in relative terms, the opposite was true. Finally, it appears that the changed monetary and economic environment in the 1980s had a marked impact on the pricing of the options embedded in extendible bonds and their relationship to the Black and Scholes model's estimated prices.