Optimal choice of crop insurance: The Case of Winter Barley in France

This paper analyzes how the agricultural insurance market is adapting to climate change, particularly as extreme weather events become more frequent and severe. We focus on the optimal decision faced by a risk-averse farmer who wants to insure their crop while making savings. They can choose between a traditional loss-based insurance, index-based insurance or a mix of both. By maximizing the farmer's CARA utility function, we show that in some cases, a mixed insurance strategy is more advantageous than a single contract. In our model, the farmer insures only part of the crop when the market interest rate is strictly positive. Demand for traditional and index insurance depends on their respective prices. Highly risk-averse farmers prefer traditional insurance. A numerical application to the French agriculture sector indicates that mean spring temperature primarily affects winter barley yield and could therefore be the main indicator for index-based insurance design. Insurance simulations using the theoretical model and the estimated results further illustrate these findings.