Given the assumption that weather risks affect crop yields, we designed a weather index insurance product for soybean producers in the US state of Illinois. By separating the entire vegetation cycle into four growth stages, we investigate whether the phase-division procedure contributes to weather–yield loss relation estimation and, hence, to basis risk mitigation. Concretely, supposing stage-variant interaction patterns between temperature-based weather index growing degree days and rainfall-based weather index cumulative rainfall, a nonparametric weather–yield loss relation is estimated by a generalized additive model. The model includes penalized B-spline (P-spline) approach based on nonlinear optimal indemnity solutions under the expected utility framework. The P-spline analysis of variance (PS-ANOVA) method is used for efficient estimation through mixed model re-parameterization. The results indicate that the phase-division models significantly outperform the benchmark whole-cycle ones either under quadratic utility or exponential utility, given different levels of risk aversions. Finally, regarding hedging effectiveness, the expected utility ratio between the phase-division contract and the whole-cycle contract, and the percentage changes of mean root square loss and variance of revenues support the proposed phase-division contract.

考虑到天气风险影响作物产量的假设，我们为美国伊利诺伊州的大豆生产商设计了天气指数保险产品。通过将整个植被周期分为四个生长阶段，我们研究了阶段划分程序是否有助于天气-产量损失关系估计，从而有助于缓解基础风险。具体而言，假设基于温度的天气指数生长度日和基于降雨量的天气指数累积降雨量之间的阶段变化相互作用模式，通过广义相加模型估计非参数天气-产量损失关系。该模型包括基于预期效用框架下非线性最优赔偿解的惩罚 B 样条（P 样条）方法。P 样条方差分析 (PS-ANOVA) 方法用于通过混合模型重新参数化进行有效估计。结果表明，在不同程度的风险厌恶情况下，无论是在二次效用还是指数效用下，相分模型都显着优于基准全周期模型。最后，关于套期保值有效性，分期合约与全周期合约之间的预期效用比率、均方根损失和收入方差的百分比变化支持了所提出的分期合约。