Generalized Linear Models in Life Insurance: Decrements and Risk factor analysis under Solvency II

The need to accurately understand the factors underlying lapse, surrender and mortality (collectively termed ‘decrements’ for the purposes of this paper) rates in life insurance is increasing because of (inter alia) the effect of International Accounting Principles, Solvency II and MCEV reporting. The aim of this paper is to investigate the use of Generalized Linear Models to capture empirical dependencies between risk factors and to understand the best factors to allow for in a correct calibration of lapse risk. After a brief description of theoretical aspects of Generalized Linear Models and their applications in analyzing for risk factors, we have investigated the lapse and surrender experience data of a large Italian bancassurer. The investigation covered the period from 1991 to 2007. The products concerned were life insurance savings policies, with a preponderance of single premium or recurrent single premium products. The case study results show in the specific case of the chosen Italian company the importance of policy duration, as expected, but also show the sensitivity of lapse rates to calendar year of exposure, to product class and to policyholder age. The work has been carried out by analysing only readily available risk factor data and could hence be substantially improved by a refinement of the underlying database. The results presented in this paper are to be interpreted as being work in progress, to be further refined in future developments.