Term structure shapes in the Hull-White model with Svensson-parameterized initial yield curves

We examine the shapes attainable by the forward and yield curve in the Hull-White model with Svensson-parameterized initial yield curves. For Nelson-Siegel-parameterized initial yield curves, we provide a complete classification of all attainable shapes and partition the parameter space and the state space according to these shapes. Our analysis relies on the theory of Tchebycheff systems and the envelope method. For Bliss- and Svensson-parameterized initial yield curves, we derive lower and upper bounds on the number of attainable local extrema. We examine the asymptotic behavior of the model and demonstrate that the yield curve attains only the shapes normal, inverse and humped with positive probability as $t\rightarrow\infty.$