The Implication of Copula-Based Models for Crop Insurance and Reinsurance Under Systemic Risk

Abstract

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The purpose of this paper is to estimate county-level aggregate crop insurance and reinsurance losses under systematic risk. The effect of dependence risk on losses assessment and insurance pricing is quantified by establishing joint distribution functions between county-level yields using different forms of multivariate copulas. The research also stresses the importance of selecting the appropriate copula form for estimating losses. This article highlights several significant findings. The estimated aggregate losses for related counties are not significantly different between the model assuming dependence (copula-based) and the model assuming independence (individual) that adheres to the equivalence principle. On the other hand, the copula-based model has a discernible effect on the estimated Value-at-Risk and Expected Shortfall for related counties. Additionally, for the different layers of the Standard Reinsurance Agreement policy, the copula-based model can measure the aggregate losses more accurately than the individual models. Furthermore, when there is obvious tail dependence in the related counties’ yields, the vine copula function form, which provides a more flexible description of the dependence, is more suitable for quantifying tail risk. As a result, insurers and governments should conduct a more comprehensive risk assessment of yield dependence when rate-making and allocating subsidies.

Keywords

• copula function
• crop insurance
• reinsurance
• actuarial fair pricing
• effective analysis