How cold is too cold? A theoretical analysis of the optimal trigger for index insurance for frost damage to crops

Abstract Crop insurance is undoubtedly an extremely valuable element in protecting agricultural businesses, but in many cases standard indemnity‐based products have had very low uptake due to high transaction costs elevating premiums to unaffordable levels. Index insurance options in which coverage is written on a publicly observable “trigger” (involving much lower transaction costs) have begun to fill the void. In almost all of the previous economics literature on index insurance, the only variable that the insurance demander is permitted to choose is the payment to be received should the index trigger value be verified. However, it is clear that the trigger value itself is an integral element in the contract, and it is an element about which the insurance demander has clear preferences. In this article, we analyze the optimal demand for index insurance under the assumption that the demander can choose both the payment to be received if the index trigger is satisfied and the trigger value itself. We find that there is always an interior solution to this problem. We also consider the market equilibria that emerge under a variety of settings in regard to the position of the insurer. The article is cast within the scope of insurance for frost damage to a crop, but all of the results are directly applicable to any peril for which a publicly observable signal exists. The article shows that allowing the demander to choose both indemnity and trigger value should increase uptake of index insurance products.