Mixture modeling segmentation and singular spectrum analysis to model and forecast an asymmetric condor-like option index insurance for Colombian coffee crops

Weather-related hazards generate unfortunate risks, especially for low-income economies, such as populations dependent on agriculture. Index insurance offers structural advantages compared with conventional insurance, including moral hazard, adverse selection, and systemic risk. It also represents a promising financial tool because of its potential to provide timely economic relief after an unusual weather event by indemnifying policyholders based on the observed value of a particular index directly related to weather parameters. Because of these advantages, this type of insurance can potentially be extended to more crop-productive regions. This study examines the possible spread of weather index insurance programs for Arabica Coffee in Colombia in the short and medium terms in aggregated regions, according to the wet and dry crop seasons. Using a short historical precipitation data from 2010 to 2019 for 163 productive zones in 11 departments located at altitudes of 990–1,890 m, we use an unsupervised technique to first cluster the observations through mixture modeling. Then, we extract through singular spectrum analysis, the signal components of precipitation of each cluster and seasons to propose a simple index insurance model which determines the immediate payoff disbursals. We particularly identify the behavior of the tendency and seasonal payoffs. Finally, we forecast the tendency components in each cluster and season to derive a ratio of future payoffs in exceedance. This ratio serves as a measure of financial risk as it represents future additional payments that are expected to be disbursed due to the tendency component. The results have important implications for designing agricultural hedging instruments for coffee producers at an individual scale or as reinsurance instruments.