Accounting for Geographic Basis Risk in Heat Index Insurance: How Spatial Interpolation Can Reduce the Cost of Risk

Abstract

Extreme heat events cause periodic damage to crop yields and may pose a threat to the income of farmers. Weather index insurance provides payouts to farmers in case of measurable weather extremes to keep production going. However, its viability depends crucially on the accuracy of local weather indices to predict yield damages from adverse weather conditions. So far extreme heat indices are poorly represented in weather index insurance. In this study we construct indices of extreme heat using observations at the nearest weather station and estimates for each county using three interpolation techniques: Inverse-distance weighting, ordinary kriging, and regression kriging. Applying these indices to insurance against heat damage to corn in Illinois and Iowa, we show that heat index insurance reduces relative risk premiums by 27-29% and that interpolated indices outperform the nearest-neighbor index by around 2-3% in terms of relative risk reduction. Further, we find that the advantage of interpolation over a nearest-neighbor index in terms of relative risk reduction increases as the sample of weather stations is reduced. These findings suggest that heat index insurance can work even when weather data is spatially sparse, which delivers important implications for insurance practice and policy makers. Further, our public code repository provides a rich toolbox of methods to be used for other, perils, crops and regions. Our results are therefore not only replicable but also constitute a cornerstone for projects to come.

Research on a Model for an Empirical Analysis of Inherent Defect Insurance Based on Ruin Theory

“…Numerous scholars have analysed the mathematical probability model and explored the characteristic changes in bankruptcy models under diferent conditions [29][30][31]. In addition, several researchers have tried applying the ruin model to specifc insurance practices and have used mathematical methods to analyse insurance risks [32][33][34][35][36][37]. Insurance ruin theory-as the basic theory of insurance actuarial science, particularly insurance risk analysis-has broad applicability in actuarial practice.…”

“…Since the probability density function of the standard normal distribution is always greater than 0, the derivative function represented by equation ( 31) is always less than 0, and the function image is monotonically decreasing, so there is no maximum value. However, it can be seen from the zero point of the second derivative expressed in equation (32) that the function has an infection point at which the convexity of the function changes. Te optimal initial reserve is determined as follows:…”

“…Terefore, highest u * 0 in the 0-2-year period does not mean that the insurance risk is the greatest. For the average initial reserve per order u 0 can be expressed as a function of the product of the claim frequency parameter λ and claim settlement amount parameter θ, and the degree of the denominator is higher in equation (32), the function is inversely proportional. Since the claim frequency parameter λ and claim settlement amount parameter θ of the 3-5-year period are both slightly larger than the values of the 0-2-year period, the optimal initial reserve u * 0 of the 3-5year period will be slightly smaller than the value of the 0-2year period.…”