The last two decades have seen a tremendous increase in the adoption of Semantic Web technologies as a result of the availability of big data, the growth in computational power and the advancement of artificial intelligence (AI) technologies. Cutting-edge semantic techniques are now able to capture sentiments more accurately in various practical applications, including economic and financial forecasting. In particular, the extraction of sentiment from news text, social media and blogs for the prediction of economic and financial variables has attracted attention in recent years. Despite many successful applications of sentiment analysis (SA) in these domains, the range of semantic techniques employed is still limited and mostly focused on the detection of sentiment at a coarse-grained level, that is, whether the sentiment expressed by the entire text of a sentence is either positive or negative. This paper proposes a novel methodology for Fine-Grained Aspect-based Sentiment (FiGAS) analysis. The aim of the approach is to identify the sentiment associated to specific topics of interest in each sentence of a document and assigning real-valued polarity scores between -1 and +1 to those topics. The proposed approach is completely unsupervised and customized to the economic and financial domains by using a specialized lexicon make available along with the source code of FiGAS. Our lexicon-based SA approach relies on a detailed set of semantic polarity rules that allow understanding the origin of sentiment, in the spirit of the recent trend on Interpretable AI. We provide an in-depth comparison of the performance of the FiGAS algorithm relative to other popular lexicon-based SA approaches in predicting a humanly annotated data set in the economic and financial domains. Our results indicate that FiGAS statistically outperforms the other methods by providing a sentiment score that is closer to one of the human annotators.