Modelling dynamic lapse with survival analysis and machine learning in CPI

In this paper, we will focus our attention on describing and predicting policyholder behaviour dynamically within the specific context of credit protection insurance (CPI). Banks, in fact, purchase this type of insurance to cover the risk that their borrowers become unable to honor their payments due to death, disability, job loss, critical illness or other causes. Given that a CPI will expire as soon as the borrower prepaid or defaulted, accurate estimates of the related assumptions are necessary to calculate a prudential premium at inception as well as the expected future profitability. The reference data are a proprietary dataset with origination and performance observations on 50,000 individuals who have taken out a loan on the US market. First, we will compare different machine learning models (i.e. logistic regression, accelerated failure time model and random survival forest) fitted on the aforementioned data in a survival analysis setting to predict default and prepayment. In particular, we will find that the random survival forest returns superior estimations regardless of the specific lapse model structure. The other element of the analysis consists of making assumptions on the market dynamics and the underlying actuarial model. The former will allow for the simulation of interest rate scenarios, while the latter will be necessary to calculate CPI profit components such as premium and reserve. The combination of lapse estimation and insurance dynamics will define the CPI profit model which we will use to determine the time value of options and guarantees varying by interest rate features.