Exploring Underlying Distributional Assumptions of Livestock Gross Margin Insurance for Dairy

Livestock Gross Margin Insurance for Dairy Cattle (LGM-Dairy) is a recently introduced tool for protecting average income over feed cost margins in milk production. In this paper we examined the assumptions underpinning the rating method used to determine premium charged for LGM-Dairy insurance contract. The first test relates to assumption of lognormality in terminal futures prices. Using high-frequency data for futures and options for milk, corn and soybean meal we estimate implied densities with flexible higher moments. Simulations indicate there is no strong evidence that imposing lognormality introduces bias in LGM-Dairy premiums. The rest of the paper is dedicated to examining dependency between milk and feed marginal distributions. LGM-Dairy rating method imposes the restriction of zero conditional correlation between milk and corn, as well as milk and soybean meal futures prices. Using futures data from 1998-2011 period we find that allowing for non-zero milk-feed correlations considerably reduces LGM-Dairy premiums for hedging profile with substantial feed amounts declared. Further examination of the nature of milk-feed dependencies reveals that Spearman’s correlation coefficient is mostly reflecting tail dependence. Using empirical copula approach we find that non-parametric method of modeling milk-feed dependence decreases LGM-Dairy premiums more than a method that allows only for linear correlation. Unlike all other situations in portfolio risk assessment where extremal dependence increases risk, in insurance risk, and reduce actuarially fair premiums.