Estimation procedures for the term structure of interest rates

Abstract

In the numerical estimation of the term structure of interest rates, one of the most common topics is the smoothness of the fitting curve, which must be combined with the precision of the fitting curve at each observed point. The spline function have been widely used in the approximation of the term structure because of the flexibility of them. This thesis, as a major point, tries to choose the smoothest curve in the set of spline functions each of which satisfies the conditions assigned by the user on the precision of the fitting curve. In order to accomplish this object, a study on spline and its application should be done. The reason why we choose a special type of spline is that, in the term structure estimation, we must be greatly concerned about the precision and the smoothness. However, as far as we know, there are no works to explain the relationship between the characteristics of the initial yield curve and the properties of spline functions. Chater 3 presentes the general form of the spline and also presents interpolation problems of initial yield curve. The chapter explains why we choose a special type of spline and how to join the selected spline to the estimation problem. Analyzing the relationship between the kont sequence and its approximation, we define a spline and introduce the adjustment process of the term structure data. measure of the smoothness or the precision of a fitted curve are appeared in this process and the chapter is finished by the settlement of the minimal interpolation problem which contains both the two measures. A general study of the term structure described in Chapter 2 offers a short review on several previous works of the continuous time models and the numerical estimation models. in this division of the numerical estimation, many researchs have used the spline fitting technique. Most of the developed methods contain cubic splines of fourth order splines filtered by their own ways, and several conditions are added to pro...