On modelling volatility and mortality for pension schemes

The purpose of this research is to develop volatility and mortality models that could be used in asset liability management in pension schemes. This study provides a comprehensive study of various advance multivariate DCC GARCH models which are used for construction of optimal portfolios in modelling asset return covariances. The effectiveness of using parametric copula in estimating portfolio risk measures are evaluated such that the DCC models are found to have better performance than any other parametric copula models. Several models were developed as extensions to existing mortality models in a single and multiple population, in particular the Lee Carter (LC) mortality model and the Common Age Effect (CAE) model by proposing a modification of singular value decomposition (SVD) and principal component analysis (PCA) methods. Complementing this, a further study on mortality model by applying a range of multivariate DCC GARCH models in modelling the mortality dependence across multiple populations is evaluated. Finally, the proposed models of volatility and mortality are applied to the pension schemes. The volatility models were fitted using multivariate DCC GARCH model to obtain the investment returns and the cohort actuarial tables were produced based on LC approach for the out-of-sample period in the UK population. The fits from the modelling of volatility and mortality were analysed on defined benefit (DB), defined contribution (DC) and hybrid schemes to evaluate the fund value and actuarial liabilities. This research underlined the important role that econometric volatility modelling and stochastic mortality modelling can play in managing pension schemes to ensure that future liabilities can be meet.