Weather insurance design with optimal hedging effectiveness

Abstract

I construct index-based weather insurance contracts with optimal hedging effectiveness for the insured or maximal profits for the insurer. In contrast to earlier work, I\nrefrain from imposing functional form assumptions on the stochastic relationship between weather and yield and from restricting attention to (piecewise) linear contracts.\nInstead, I derive the shape of the optimal weather insurance contracts empirically by non-parametrically estimating yield distributions conditional on weather. I find that the optimal pay-off structure is non-linear for the entire range of weather realizations. I measure risk reduction of optimal weather insurance contracts for different weather indices and levels of risk aversion. Considering profit-maximizing contracts, I find that at modest levels of risk aversion (coefficient of relative risk aversion around 2), a loading factor of 10% of the fair premium is possible such that the insurance contract\nremains attractive for the insured. With higher levels of risk aversion, loading of more than 50% becomes possible.