A Probabilistic Paradigm for the Parametric Insurance of Natural Hazards

There is a pressing need for simple and reliable risk transfer mechanisms that can pay out quickly after natural disasters without delays caused by loss estimation, and the need for long historical claims records. One such approach, known as parametric insurance, pays out when a key hazard variable exceeds a predetermined threshold. However, this approach to catastrophe risk, based on making deterministic binary predictions of loss occurrence, is susceptible to basis risk (mismatch between payouts and realized losses). A more defensible approach is to issue probabilistic predictions of loss occurrence, which then allows uncertainty to be properly quantified, communicated, and evaluated. This study proposes a generic probabilistic framework for parametric trigger modeling based on logistic regression, and idealized modeling of potential damage given knowledge of a hazard variable. We also propose various novel methods for evaluating the quality and utility of such predictions as well as more traditional trigger indices. The methodology is demonstrated by application to flood-related disasters in Jamaica from 1998 to 2016 using gridded precipitation data as the hazard variable. A hydrologically motivated transformation is proposed for calculating potential damage from daily rainfall data. Despite the simplicity of the approach, the model has substantial skill at predicting the probability of occurrence of loss days as demonstrated by traditional goodness-of-fit measures (i.e., pseudo-R2 of 0.55) as well as probabilistic verification diagnostics such as receiver operating characteristics. Using conceptual models of decisionmaker expenses, we also demonstrate that the system can provide considerable utility to involved parties, e.g., insured parties, insurers, and risk managers.