ESTIMATION OF THE TERM STRUCTURE OF INTEREST RATES VIA CUBIC EXPONENTIAL SPLINE FUNCTIONS

This dissertation investigates a proposed solution to the problem of erratic forward interest rate curves estimated with the spline function approximation technique. Imposing proper boundary conditions on the estimated discount function at the longest maturity observed in the data set at an asymptotic value rather than letting it fluctuate in an unreasonable manner.; McCulloch (1975) used unconstrained ordinary spline model to estimate yield curves. However, his unconstrained spline model produces forward curve which presents erratic behavior at the long end.; Vasicek and Fong (1982) tackled this problem by first performing an exponential transformation on maturity so as to map the original maturity interval of zero to infinity onto the finite interval of zero to one. They then forced the fitted discount function to cut the transformed maturity axis at 1. They showed that this forced the segment of the forward curve beyond the longest observed maturity to eventually settle at an asymptote. Nevertheless, since the asymptotic forward interest rate was only weakly related to the data points, Vasicek and Fong's boundary condition did not necessarily eliminate the erratic behavior of the forward curve at the long maturity.; In this dissertation, we employ a set of basis functions to structure the spline model. Such model is used to fit the discount function only up to the longest observed maturity. A straight line is then spliced to the spline-fitted discount function beyond that point. Two constraints are imposed at the junction of the spline-fitted and linear portions of the estimated discount function such that these two segments are joined together smoothly.; Two sets of Maximum-likelihood-ratio tests are conducted where the Vasicek and Fong's model and the McCulloch and Chen's model are tested against the unconstrained exponential spline model respectively. In both cases, the constrained models perform better than the unconstrained model.