## Bayesian smoothing spline models and their application in estimating yield curves

##### Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] The term structure of interest rates, also called the yield curve, is the series of interest rates ordered by term to maturity at a given time. The smoothing spline as a nonparametric regression method has been used widely for fitting a smooth curve due to its flexibility and smoothing properties. In this dissertation, a class of Bayesian smoothing spline models is developed for the yield curve estimation under different scenarios. These include the Bayesian smoothing spline model for estimating the Treasury yield curves, the Bayesian multivariate smoothing spline model for estimating multiple yield curves jointly, the Bayesian adaptive smoothing spline model for dealing with the yield data in which the smoothness varies significantly, the Bayesian smoothing spline model for extracting the zero-coupon yield curve from coupon bond prices, and the Bayesian thin-plate splines for modeling the yield curves on both the calendar time and the maturity. In addition, the Bayesian model selection in the smoothing spline models is
developed to test the nonlinearity of the yield curves.

##### Degree

Ph. D.