Flexible Modeling of Multivariate Risks in Pricing Margin Protection Insurance: Modeling Portfolio Risks with Mixtures of Mixtures

Margin Protection Programs (MPPs) are relatively new insurance plans that have been introduced and made available by the USDA’s Risk Management Agency (RMA). These programs were initially implemented for livestock and dairy producers, and were subsequently extended to cover other agricultural products such as corn, rice, soybeans, and wheat. 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. This paper examines the structure and rating of margin protection insurance policies. In particular, the paper considers a broad class of high-dimensional copula models that parameterize the dependence among multivariate sources of risks. To efficiently and accurately determine actuarially fair policy premiums, it is necessary to first model the joint distribution function of input and output prices. This task can be effectively carried out using copula methods. A variety of copula methods, including Archimedean Copulas (ACs), Mixture Copulas (MCs), and Vine Copulas (VCs) are used to analyze 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 paper 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. Goodness-of-fit tests generally reject conventional approaches based upon log-normally distributed marginals and Gaussian copulas. In this paper, several reasons are identified to explain why the common methods being currently employed to determine policy premiums might not be adequate, realistic, or sufficiently flexible to take into account the multivariate aspects of risks involved in farming operations. To this end, the present paper investigates the underlying assumptions based on which the MPP policy premiums are determined. It is argued that assumptions made in pricing risks may induce important distortions in the production and marketing decisions of producers. It is also noted that precise measurement of the marginal densities for individual random variables is essential for accurately pricing a portfolio of multivariate risks. Finally, implications for the ever-expanding offerings of publicly-subsidized agricultural insurance mechanisms are offered.