Plant growth stages and weather index insurance design

Research output: Contribution to journalResearch articleContributedpeer-review


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.


Original languageEnglish
Pages (from-to)438-458
Number of pages21
JournalAnnals of actuarial science
Issue number3
Publication statusPublished - 3 Nov 2023

External IDs

ORCID /0000-0002-8909-4861/work/149081752



  • generalized additive model, nonlinear indemnity, plant growth stages, PS-ANOVA, Weather index insurance

Library keywords