Tailored to the extremes: Quantile regression for index‐based insurance contract design

A new approach for weather index‐based insurance design based on Quantile Regression (QR) to condition the yield‐index dependency is developed and compared to standard regression technique. Three conceptual different risk measures, i.e., Expected Utility, Expected Shortfall and a Spectral Risk Measure, are used to evaluate the risk reducing properties of these contracts. Our findings show that QR is much more powerful in establishing the yield‐index dependency and lead for all risk measures to a higher risk reduction than the standard technique ordinary least squares (OLS). Thus, QR leads to a more efficient contract design, which is beneficial for both, the insurer (smaller remaining risk) and the insured (higher demand and willingness to pay). Our empirical application is based on a 31 years long time series of wheat yield data from Northern Kazakhstan.