Modeling Dependence in the Design of Whole Farm---A Copula-Based Model Approach

The objective of this study is to evaluate and model the risks of corn and soybean production. This study focuses on the risk of revenue variability that arises from changes in prices, yields shortfalls or both. There are several models for price and yield risk factors for corn and soybeans. For instance, yield risks can be modeled by a family of Beta distributions, whereas price shocks can be modeled by log-normal distributions. In order to develop a multivariate model that preserves a given set of marginals, a copula approach can be used to characterize the joint yield and price risk of corn and soybeans, which are usually highly correlated. The copula approach has been spurred by the recent developments in the whole farm insurance (WFI), resulting in an increasing need for the modeling of multivariate risk factors and their interaction. As a part of the study, various copula models are investigated for their suitability in modeling yield and price risks. Finally, the proposed copula approach is illustrated with simulated data to calculate the premium rate of the whole farm insurance. Results show that WFI is superior to crop-specific insurance with premia 36% cheaper than the latter.