Weather insurance design with optimal hedging effectiveness

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 refrain from imposing functional form assumptions on the stochastic relationship between weather and yield and from restricting attention to (piecewise) linear contracts. Instead, 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 remains attractive for the insured. With higher levels of risk aversion, loading of more than 50% becomes possible.