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.