Stochastic models for asset and liability modelling in South Africa or elsewhere

Abstract

Research in the area of stochastic models for actuarial use in South Africa is limited to relatively few publications. Until recently, there has been little focus on actuarial stochastic models that describe the empirical stochastic behaviour of South African financial and economic variables. A notable exception is Thomson’s (1996) proposed methodology and model. This thesis presents a collection of five papers that were presented at conferences or submitted for peer review in the South African Actuarial Journal between 1996 and 2006. References to subsequent publications in the field are also provided. Such research has implications for medium and long-term financial simulations, capital adequacy, resilience reserving and asset allocation benchmarks as well as for the immunization of short-term interest rate risk, for investment policy determination and the general quantification and management of risk pertaining to those assets and liabilities. This thesis reviews Thomson’s model and methodology from both a statistical and economic perspective, and identifies various problems and limitations in that approach. New stochastic models for actuarial use in South Africa are proposed that improve the asset and liability modelling process and risk quantification. In particular, a new Multiple Markov-Switching (MMS) model framework is presented for modelling South African assets and liabilities, together with an optimal immunization framework for nominal liability cash flows. The MMS model is a descriptive model with structural features and parameter estimates based on historical data. However, it also incorporates theoretical aspects in its design, thereby providing a balance between purely theoretical models and those based only on empirical considerations.