The use of weather index insurances is subject to spatial basis risk, which arises from the fact that the location of the user's risk exposure is not the same as the location of any of the weather stations where an index can be measured. To gauge the effectiveness of weather index insurances, spatial interpolation techniques such as kriging can be adopted to estimate the relevant weather index from observations taken at nearby locations. In this paper, we study the performance of various statistical methods, ranging from simple nearest neighbor to more advanced trans-Gaussian kriging, in spatial interpolations of daily precipitations with data obtained from the US National Oceanic and Atmospheric Administration. We also investigate how spatial interpolations should be implemented in practice when the insurance is linked to popular weather indexes including annual consecutive dry days ($CDD$) and maximum five-day precipitation in one month ($MFP$). It is found that although spatially interpolating the raw weather variables on a daily basis is more sophisticated and computationally demanding, it does not necessarily yield superior results compared to direct interpolations of $CDD$/$MFP$ on a yearly/monthly basis. This intriguing outcome can be explained by the statistical properties of the weather indexes and the underlying weather variables.

翻译：天气指数保险的使用受限于空间基差风险，该风险源于风险暴露位置与可测量指数的气象站位置不一致。为评估天气指数保险的有效性，可采用克里金等空间插值技术，根据邻近站点的观测数据估算相关天气指数。本文基于美国国家海洋和大气管理局的数据，研究从简单最近邻法到更先进的跨高斯克里金法等统计方法对日降水量空间插值的表现。同时，探讨当保险与常用天气指数（包括年连续干旱天数CDD和月最大五日降水量MFP）挂钩时，实际中如何实施空间插值。结果表明，尽管对原始天气变量进行逐日空间插值更为复杂且计算要求更高，但相较于对CDD/MFP进行年/月直接插值，并未必然产生更优结果。这一有趣现象可通过天气指数及其基础天气变量的统计特性得到解释。