Forecasting mortality rates and modeling longevity risk using lee carter model

Abstract

The retirement benefits provided by annuity providers and pension plans imply are often guaranteed until the death of the pensioners. Trends in mortality/longevity have clearly emerged as a result of increase in life expectancy/ reduction in mortality rates at old age. This has necessitated academicians and actuaries to focus their interest in the field of mortality and longevity risks in particular. The new NSSF Act No. 45 of 2013established a pension fund that is mandatory for all workers in the formal economy as opposed to a provident fund. This exposes the annuity providers to longevity risk among other risks when the scheme members retire. Appropriate modelling tools or projected life tables are needed for pricing and reserving. In particular the use of stochastic models that allows for various risk causes and components and the relevant impact on portfolio results as opposed to the deterministic models that were only based on the expected present values. For the purpose of this project, I am using the Lee- Carter Model proposed by Lee and Carter in 1992 to fit mortality rates, forecast mortality trends in an ARIMA framework and then obtain the life expectancy projections. As regards to the longevity risk, I consider the possibility of changing the annuity benefits or calculating the annuity benefits by relating the benefits to the experienced mortality, or to updated mortality forecasts therefore calculating the actuarial present value on annuity .