Consistency of extended Nelson-Siegel curve families with the Ho-Lee and Hull and White short rate models

TL;DR

This paper investigates how the initial Nelson-Siegel interest rate curves evolve under the Ho-Lee and Hull-White models, showing that the resulting forward curves remain within an extended Nelson-Siegel family.

Contribution

It demonstrates that the forward curve process in these models preserves a parametric family of extended Nelson-Siegel curves, linking curve fitting and interest rate modeling.

Findings

Forward curves stay within an extended Nelson-Siegel family.

The models produce parametric families of curves consistent with initial Nelson-Siegel curves.

The evolution maintains the structure of the initial term structure.

Abstract

Nelson and Siegel curves are widely used to fit the observed term structure of interest rates in a particular date. By the other hand, several interest rate models have been developed such their initial forward rate curve can be adjusted to any observed data, as the Ho-Lee and the Hull and White one factor models. In this work we study the evolution of the forward curve process for each of this models assuming that the initial curve is of Nelson-Siegel type. We conclude that the forward curve process produces curves belonging to a parametric family of curves that can be seen as extended Nelson and Siegel curves.