A Unique Unconditionally Arbitrage-Free Solution to the Term Structure of Interest Rates

This paper points out that the fundamental partial differential equation (PDE) implies that the drifts of the underlying processes are irrelevant, regardless whether the state factors are tradable or not. Since the simple boundary condition for default-free discount bonds can be satisfied by a linear discount function, the variances and covariances of the underlying processes are also irrelevant. This paper proves that the linear solution is unique, which indicates that the bond market has an unconditionally arbitrage-free equilibrium. The unique linear solution, namely, the Exponential Polynomial (EP) model, is equivalent to the Exponential Spline model of Vasicek and Fong (1982) without spline fitting. The empirical results support the model. JEL Classification: G12.