Mortality Risk. Incorporating the New Seasonal-Ageing Index (SAI) into a Pricing Strategy

Insurance companies use annual life tables to manage mortality risks despite intra-annual mortality risks showing sub-annual fluctuations. The difficulty of (accurately) measuring and computing these fluctuations is likely behind this decision. The research carried out by [5], however, offers new opportunities by developing a methodology that, for the first time in the literature, allows actuaries and statisticians to derive quarterly life tables from annual tables simply by using the so-called SAI (Seasonal-Ageing Indexes) coefficients. SAIs capture mortality risks taking into account both source of fluctuations, age and calendar quarters. This paper aims to discern the implications of using an approach based on SAIs and study how the new methodology could be employed in a competitive market where different insurance companies operate. On the one hand, we exemplify the new procedure on a real insurance portfolio by calculating premiums for different quarters. This gives, for each age and calendar quarter, the distance (measured in euros) between using annual and SAI-quarterly life tables. On the other hand, we study the market opportunities that the new methodology offers by simulating a two-company market, where one of the companies incorporates SAI-quarterly tables in its pricing processes. We analyse the impact of the use of these different market strategies on profit and loss accounts of both companies. The results of this research highlight some of the practical advantages of using the SAI-based approach.