Flexible modelling of multivariate risks in pricing margin protection insurance: modelling portfolio risks with mixtures of mixtures

Margin Protection Programs (MPPs) are relatively new insurance plans, introduced by USDA’s Risk Management Agency (RMA). The attractiveness of these risk management instruments lies in the fact that the financial stability of agricultural production and farming operations is more dependent on margins than solely revenues, which neglect production costs, as is the case for Revenue Protection Programs (RPPs). This article examines the structure and rating of margin protection insurance policies by considering a broad class of high-dimensional copula models that parameterize the dependence among multivariate sources of risks. A variety of copula methods, including Archimedean Copulas (ACs), Mixture Copulas (MCs), and Vine Copulas (VCs) are used to analyse the dependence structure between revenues and input costs. In terms of methodology, flexible mixtures of parametric distributions are applied to characterize marginal densities, and likewise flexible mixtures of alternative copulas are used to model dependence. This article also argues that the rating methodology that accounts for irregular and anomalous features of dependence such as asymmetry, non-linearity, non-ellipticity, and tail dependence between input prices and output prices can result in more accurate premiums, and therefore, can increase the hedging effectiveness of the MPPs and the market efficiency in the US crop insurance market.