Using Bayesian Kriging for Spatial Smoothing in Crop Insurance Rating

Rating insurance policies depends on the probability of events in the tail of a distribution. A method to measure such tail-related risk based on Extreme Value Theory could potentially improve insurance rating. It is also widely agreed that there is a spatial structure to crop yield distributions. Considering the spatial structure may provide more precisely rated policies. In this context, this research provides two contributions in rating area yield crop insurance. One is to provide a method that fits the tail of crop yield distributions using the Generalized Pareto Distribution (GPD), a member of the family of extreme value distributions that models only the tail of the distribution. The second is to estimate parameters of the distribution using a Bayesian Kriging approach that provides spatial smoothing of GPD parameters. The proposed model provides estimates of the spatial structure across regions such as the maximum distance of the spatial effect. Based on an out-of-sample performance game between a private insurance company and the federal agency the proposed model provides considerable improvement, particularly when rating deeper tail probability.