Parametric estimation of latent default frequency in credit insurance

In credit insurance practice, insurers must address the lack of information that affects their knowledge of present and past underwritten risks. In this context, classical frequency estimators, although effectively employed in various financial and actuarial applications to measure absorbing events, are not suitable. Given that default frequency estimation is affected by the temporal distribution of the invoices issued by an insured seller during the credit insurance coverage period, this study proposes a behavioral model to describe the commercial relationships between insured sellers and their buyers. The model is parsimonious and easily calibrated based on historical data. A closed-form estimator for the number of default events is introduced by the model parameterization, allowing for a precise inference of the actual default frequency over a given period, which compensates for the bias caused by unobserved events. The proposed method is numerically tested against the simultaneous presence of multiple behavioral types, whose composition may change over time, but still enables a credit insurance company to accurately estimate claim and default probabilities.