Long-term interest rates and consol bond valuation

Abstract

This article presents a Gaussian three-factor model of the term structure of interest rates which is Markov and time-homogeneous. The model captures the whole term structure and is particularly useful in forward simulations for applications in long-term swap and bond pricing, risk management and portfolio optimization. Kalman filter parameter estimation uses EU swap rate data and is described in detail. The yield curve model is fitted to data up to 2002 and assessed by simulation of yield curve scenarios over the next 2 years. It is then applied to the valuation of callable floating rate consol bonds as recently issued by European banks to raise Tier 1 regulatory capital over the subsequent period from 2005 to 2007.