Yield Curve Construction with Tension Splines

Abstract

Polynomial splines are popular in the estimation of discount bond term structures, but suffer from well-documented problems with spurious inflection points, excessive convexity, and lack of locality in the effects of input price perturbations. In this paper, we address these issues through the use of shape-preserving splines from the class of generalized tension splines. Our primary focus is on the classical hyperbolic tension spline which we derive non-parametrically from a penalized least squares criterion, but extensions to generalized tension splines - such as rational splines and exponential splines - are also covered. Our methodology allows both for best-fitting of noisy bonds and for the construction of an exact interpolatory term structure to a set of liquid instruments. Throughout, we work with a local tension B-spline basis, and support both fully non-parametric and user-imposed knot location strategies.