This paper addresses the prediction of the total damage costs brought on by a drought episode under the French "Régime de Catastrophes Naturelles''. Due to the specificity of this natural disaster compensation scheme, an early prediction of the cost of a disaster is needed to improve strategic decisions. Taking advantage of the access, thanks to a partnership with the Mission Risques Naturels, to a database of natural disaster claims fed by the major French insurance companies, we combine the information of drought event claims contained in this database with meteorological and socioeconomic data to achieve a more comprehensive knowledge of the exposure. Our prediction approach relies on the comparison of different statistical models and machine learning algorithms. To improve the prediction performance, we propose an aggregation of the different models. Since the main difficulty encountered is imbalanced data as a large majority of cities are not affected by a drought event, the predictions are assessed by F1-scores and Precision and Recall curves.