Conversational AI chatbots are transforming industries by streamlining customer service, automating transactions, and enhancing user engagement. However, evaluating these systems remains a challenge, particularly in financial services, where compliance, user trust, and operational efficiency are critical. This paper introduces a novel evaluation framework that systematically assesses chatbots across four dimensions: cognitive and conversational intelligence, user experience, operational efficiency, and ethical and regulatory compliance. By integrating advanced AI methodologies with financial regulations, the framework bridges theoretical foundations and real-world deployment challenges. Additionally, we outline future research directions, emphasizing improvements in conversational coherence, real-time adaptability, and fairness.