Financial event entity extraction is a crucial task for analyzing market dynamics and building financial knowledge graphs, yet it presents significant challenges due to the specialized language and complex structures in financial texts. Traditional approaches often rely on sequence labeling models, which can struggle with long-range dependencies and the inherent complexity of extracting multiple, potentially overlapping entities. Motivated by the advanced language understanding and generative capabilities of Large Language Models (LLMs), we propose a novel method that reframes financial event entity extraction as a text-to-structured-output generation task. Our approach involves fine-tuning a pre-trained LLM using Parameter-Efficient Fine-Tuning (PEFT) to directly generate a structured representation, such as a JSON object, containing the extracted entities and their precise character spans from the input text. We evaluate our method on the challenging CCKS 2019 Financial Event Entity Extraction dataset, comparing its performance against strong sequence labeling baselines, including SEBERTNets and sebertNets. Experimental results demonstrate that our generative LLM method achieves a new state-of-the-art F1 score on this benchmark, significantly outperforming previous methods. Through detailed quantitative analysis across event types, entity types, and instance complexity, as well as human evaluation, we show that our approach is more effective at handling the nuances of financial text and extracting high-quality entities. This work validates the potential of applying generative LLMs directly to complex, domain-specific information extraction tasks requiring structured output.