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.

在本文中，我们将重点关注在信用保护保险 (CPI) 的特定背景下动态描述和预测保单持有人的行为。事实上，银行购买这种类型的保险是为了保障借款人因死亡、残疾、失业、重大疾病或其他原因而无法偿还贷款的风险。鉴于 CPI 将在借款人预付或违约后立即到期，因此需要对相关假设进行准确估计，以计算开始时的审慎溢价以及预期的未来盈利能力。参考数据是专有数据集，其中包含对在美国市场上贷款的 50,000 个人的起源和绩效观察。首先，我们将比较不同的机器学习模型（即逻辑回归、加速故障时间模型和随机生存森林）在生存分析设置中拟合上述数据以预测违约和预付款。特别是，我们会发现无论特定的失效模型结构如何，随机生存森林都会返回更好的估计。分析的另一个要素包括对市场动态和基础精算模型的假设。前者将允许模拟利率情景，而后者将需要计算 CPI 利润组成部分，例如溢价和准备金。失效估计和保险动态的结合将定义 CPI 利润模型，我们将使用该模型来确定因利率特征而变化的期权和担保的时间价值。