Term structure shapes and their consistent dynamics in the Svensson family

TL;DR

This paper classifies all possible shapes of the forward and yield curves within the Svensson family, analyzes their dynamic evolution under no-arbitrage conditions, and shows long-term dominance of simple shapes.

Contribution

It provides a complete classification of attainable shapes in the Svensson family and characterizes their consistent dynamic evolution under no-arbitrage constraints.

Findings

Complete classification of attainable shapes

Certain complex shapes cannot persist indefinitely

Long-run dominance of inverse or normal curves

Abstract

We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the parameter space of each family according to these shapes. Building upon these results, we then examine the consistent dynamic evolution of the Svensson family under absence of arbitrage. Our analysis shows that consistent dynamics further restrict the set of attainable shapes, and we demonstrate that certain complex shapes can no longer appear after a deterministic time horizon. Moreover a single shape (either inverse of normal curves) must dominate in the long-run.