Default-free bond futures and options on default-free bond futures: Theoretical and empirical investigation

This study investigates the pricing behaviors of default-free bond futures and American options on default-free bond futures based on the framework of Brennan and Schwartz (1979). In their model, the state space of interest-rate-dependent claims is spanned by the instantaneous spot interest rate and the long-term consol rate. This design is chosen to incorporate the features of interest-rate-dependent claims and to avoid inconsistencies in other pricing models for general assets. This study assumes that the logarithm of these two factors follow a linear transformation of an Ornstein-Uhlenbeck process. The prices of these contingent claims are solutions to a set of partial different equations subject to proper boundary conditions. As there is no closed form solutions to these equations, a finite-difference method, line-hopscotch method, is employed.