Stochastic investment models for actuarial use in the UK

Abstract

The objective of this thesis is to construct a stochastic term structure model for actuarial use in the UK. The starting point of this study is the Wilkie investment model (1995). We review the Wilkie model by updating the data and re-estimating the parameters. Then, we focus on the interest rate part of the model and construct a model for the entire term structure. We model the UK nominal spot rates, real spot rates and implied inflation spot rates considering the linkage between their term structures and some macroeconomic variables, in particular, realised inflation and output gap. We fit a descriptive yield curve model proposed by Cairns (1998) to fill the missing values in the yield curve data provided by the Bank of England by changing the fixed parameters (exponential rates) in the model to find the best set of parameters for each data set. Once the Cairns model is fitted to the UK yield curves we apply principal component analysis (PCA) to the fitted values to decrease the dimension of the data by extracting uncorrelated variables. Applying PCA to the fitted values we find three principal components which correspond roughly with ‘level’, ‘slope’ and ‘curvature’ for each yield curve. We explore the bi-directional relations between these principal components and the macroeconomic variables to construct ‘yield-only’ and ‘yield-macro’ models. We also compare the ‘yield-macro’ model with the Wilkie model.