Modelling spatial correlation between earthquake insured losses in New Zealand: a mixed-effects analysis

Earthquake insurance is a critical risk management strategy that contributes to improving recovery and thus greater resilience of individuals. Insurance companies construct premiums without taking into account spatial correlations between insured assets. This leads to potentially underestimating the risk, and therefore the exceedance probability curve. We here propose a mixed-effects model to estimate losses per ward that is able to account for heteroscedasticity and spatial correlation between insured losses. Given the significant impact of earthquakes in New Zealand due to its particular geographical and demographic characteristics, the government has established a public insurance company that collects information about the insured buildings and any claims lodged. We thus develop a two-level variance component model that is based on earthquake losses observed in New Zealand between 2000 and 2021. The proposed model aims at capturing the variability at both the ward and territorial authority levels and includes independent variables, such as seismic hazard indicators, the number of usual residents, and the average dwelling value in the ward. Our model is able to detect spatial correlation in the losses at the ward level thus increasing its predictive power and making it possible to assess the effect of spatially correlated claims that may be considerable on the tail of loss distribution.