Modelling and Forecasting Mortality Rates for a Life Insurance Portfolio

Predicting and understanding longevity have always been a major concern in the fields of demography and actuarial science. Accurate mortality projections at the country level enable governments to address issues such as the structure of pension schemes, public healthcare policies, or even solve macroeconomics problems. Similarly, precise mortality forecast at the individual firm level are essential for insurance companies to effectively price their life insurance products, establish reserve funds, and calculate their Solvency Capital Requirement (SCR). However, understanding mortality at the company level involves challenges due to a lack of sufficient large datasets which makes impossible to fit the most popular mortality models in the actuarial literature. Consequently, insurance companies tend to employ simpler methods which often involves the underestimation (overestimation) of mortality (longevity) in saving products and hence, placing too high margins on their estimates, resulting in a higher cost of solvency capital (SCR) and lower profitability. The objective of this paper is to fit and forecast the mortality of the insured population using various procedures that take into account the differences between the insured and national populations. For this purpose, we will recover the piggy-back methodology, whilst introducing a novel alternative approach. The paper provide a numerical illustration of how these methodologies work using data from a Spanish life insurance company. Additionally, we assess the potential impact of applying these proposals on SCR for this particular portfolio.