Using copulas for rating weather index insurance contracts

This study develops a methodology for a copula-based weather index insurance design. Because the copula approach is better suited for modeling tail dependence than the standard linear correlation approach, its use may increase the effectiveness of weather insurance contracts designed to provide protection against extreme weather events. In our study, we employ three selected Archimedean copulas to capture the left-tail dependence in the joint distribution of the farm yield and a specific weather index. A hierarchical Bayesian model is applied to obtain consistent estimates of tail dependence using relatively short time series. Our empirical results for 47 large grain-producing farms from Kazakhstan indicate that, given the choice of an appropriate weather index to signal catastrophic events, such as a severe drought, copula-based weather insurance contracts may provide significantly higher risk reductions than regression-based indemnification schemes.