On the Reconciliation of the Extended Nelson-Siegel and the Extended Vasicek Models (with a View Towards Swap and Swaption Valuation)

Abstract

Extended Nelson-Siegel models are widely used by e.g. practitioners and central banks to estimate current term structures of riskless zero-coupon interest rates, whereas other models such as the extended Vasicek model (a.k.a. the Hull-White model) are popular for pricing interest rate derivatives. This paper establishes theoretical consistency between these two types of models by showing how to specify the extended Vasicek model such that its implied initial term structure curve precisely matches a given extended Nelson-Siegel specification. That is, we show how to reconcile the two classes of models at the initial time point (and here only). A case study and some illustrative numerical examples involving swaps and swaption pricing are provided at the end of the paper.