## 1 Introduction  
Low-income economies are severely affected by climate change, limiting sustainable development [1]. These effects are strengthened in regions with underdeveloped financial services [2, 3]. Unusual weather events lead to disruptions in worldwide food security [4]. According to recent studies, the effects of climate change, such as droughts and extreme heat conditions, have reduced the yield of staple crops worldwide by approximately 10% [5, 6]. Agriculture in Colombia is one of the most significant socioeconomic sectors, contributing to 7.4% of the GDP [7]. Some of Colombia's main agricultural products are coffee, corn, potatoes, and palm oil, among others. According to the National Agricultural Survey, ENA 2019, the total production recorded was estimated at more than 63 million tons, 67% of which corresponds to the agro-industrial product group [8]. The export of high-value crops such as coffee accounts for a sizeable portion of the GDP total. In 2020, coffee was the third most exported product in Colombia, with a value of $2.54 billion (about $8 per person in the US), and was ranked as the fourth largest coffee-exporting country in the world [9]. Nevertheless, according to the World Bank [10], Colombia is highly exposed to hydrometeorological events, known as El Nino and La Nina. These weather events result in drought or excess rainfall which directly impact the agricultural sector and affect the country's GDP. In 2010/11, La Nina's damages were estimated at 2% of GDP and about 3.5 million people were affected [10]. It is estimated that these changes in the amount of precipitation in the next 30 years will harm coffee crops [11]. Several studies have demonstrated a direct correlation between time series analysis and climate change [12,13]. These studies allow for the identification of ways to mitigate the consequences of climate change on agriculture. Trends in agrometeorological and hydrological data sets are frequently evaluated using the nonparametric Mann-Kendall test [14, 15, 16]. This test allows researchers to determine the significance of a time series trend of weather variables [17]. \"Agricultural index insurance is a financial tool for risk management that has demonstrated promise for encouraging economic development and resilience\" [18]. The main difference between this insurance and standard insurance is that payouts are based on the measure of climate variables such as rainfall and temperature. The values across which indemnity payments are made in this type of insurance are established by set thresholds and restrictions. Thresholds provide the starting point for indemnity payments. Once the threshold is met, the payout grows steadily as the index's value approaches its limit or maximum indemnity [19]. Weather index insurance offers advantages and shortcomings (Table 1). To highlight some points, index insurance is advantageous as it overcomes problems of traditional insurance such as moral hazard, adverse selection, and high costs; in addition, it can be measured remotely [26]. Despite these advantages, in index insurance, basic risk arises when the measurement does not match with actual losses because of poorly designed tools [26] or if the distance between the index measurement location and the crop's location is far [20]. One way to handle this risk is by using data or images based on satellites. For instance, payouts can be based on a Normalized Difference Vegetation Index (NDVI), which allows for estimating vegetation conditions from a color map showing relative biomass [27]. Nevertheless, NDVI sometimes does not include site calibration, and so should not be widely used in the design of index-based insurance products [28]. The benefits it offers to individual farmers are limited, so there may be more advantages to using a reinsurance tool used by corporations that have a relationship with many agricultural producers, agricultural banks, or cooperatives [21,22].