Mixture Gaussian Time Series Modeling of Long-term Market Returns

Stochastic modeling of investment returns is an important topic for actuaries who deal with variable annuity and segregated fund investment guarantees. The traditional lognormal stock return model is simple, but it is generally less appealing for longer-term problems. In recent years, the use of regime-switching lognormal (RSLN) processes for modeling maturity guarantees has been gaining popularity. In this paper we introduce the class of mixture Gaussian time series processes for modeling long-term stock market returns. It offers an alternative class of models to actuaries who may be experimenting with the RSLN process. We use monthly data from the Toronto Stock Exchange 300 and the Standard and Poor’s 500 indices to illustrate the mixture time series modeling procedures, and we compare the fits of the mixture models to the lognormal and RSLN models. Finally, we give a numerical example comparing risk measures for a simple segregated fund contract under different stochastic return models.