How Should We Value Agricultural Insurance Contracts

We argue that existing agricultural insurance valuation models are limited either because they are not complete equilibrium models that price the non-diversifiable risk involved in issuing insurance contracts, or they assume complete markets which appears at odds with most applications of agricultural insurance. We also propose two new incomplete market models and derive an insurance valuation formula for each under the assumption of constant relative risk aversion preferences and lognormally distributed random variables. The two models differ in the way they treat trade in insurance contracts, with one model allowing insurers and insureds to trade freely on a liquid secondary market, while the other requires insurance firms to act as brokers between insureds (farmers) and the capital market (those who bear the non-diversifiable risk). The two models lead to different valuation formulas and several interesting insights are obtained by comparing our valuation formulas with those used in the existing literature.