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A yield-only model for the term structure of interest rates

Published online by Cambridge University Press:  26 November 2013

Şule Şahin ,
Andrew J.G. Cairns ,
Torsten Kleinow  and
A. David Wilkie
Şule Şahin*
Affiliation:
Department of Actuarial Sciences, Hacettepe University, Ankara, TURKEY
Andrew J.G. Cairns
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University and Maxwell Institute, Edinburgh, UK
Torsten Kleinow
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University and Maxwell Institute, Edinburgh, UK
A. David Wilkie
Affiliation:
Department of Actuarial Mathematics and Statistics, Heriot-Watt University and Maxwell Institute, Edinburgh, UK
*
*Correspondence to: Şule Şahin, Department of Actuarial Sciences, Hacettepe University, Ankara, TURKEY. E-mail: sule@hacettepe.edu.tr
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Abstract

This paper develops a term structure model for the UK nominal, real and implied inflation spot zero-coupon rates simultaneously. We start with fitting a descriptive yield curve model proposed by Cairns (1998) to fill the missing values for certain given days at certain maturities in the yield curve data provided by the Bank of England. We compare four different fixed ‘exponential rate’ parameter sets and decide the set of parameters which fits the data best. With the chosen set of parameters we fit the Cairns model to the daily values of the term structures. By applying principal component analysis on the hybrid data (Bank of England data and fitted spot rates for the missing values) we find three principal components, which can be described as ‘level’, ‘slope’ and ‘curvature’, for each of these series. We explore the relation between these principal components to construct a ‘yield-only’ model for actuarial applications. Main contribution of this paper is that the models developed in the paper enable the practitioners to forecast three term structures simultaneously and it also provides the forecast for whole term structures rather than just short and long end of the yield curves.

Type
Papers
Information
Annals of Actuarial Science , Volume 8 , Issue 1 , March 2014 , pp. 99 - 130
Copyright
Copyright © Institute and Faculty of Actuaries 2013 

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