This work estimates yield losses due to drought events in mountain grasslands in north-eastern Italy, laying the groundwork for index-based insurance. Given the high correlation between Leaf Area Index (LAI) and grassland yield, we exploit LAI as a proxy for yield. We estimate LAI by the Sentinel-2 biophysical processor and we compare different gap-filling methods, including time-series interpolation and fusion with Sentinel-1 SAR data. We derive a Forage Production Index (FPI) as the growing season cumulate of the daily product between LAI and a meteorological water stress coefficient. Finally, we calculate the drought index as the anomaly of FPI. The validation of Sentinel-2 LAI with ground measurements showed RMSE of 0.92 [m2 m-2] and R2 of 0.81, on average over all the measurement sites. The comparison between FPI and yield showed R2 of 0.56 at the pixel scale and R2 of 0.74 at the parcel scale. The developed prototype FPI index was used at the end of the growing season of the year 2022 for calculating the payments of an experimental insurance scheme that was proposed to a group of farmers in Trentino-South Tyrol.