Nowadays, many mechanisms exist to perform authentication, such as text passwords and biometrics. However, reasoning about their relevance (e.g., the appropriateness for security and usability) regarding the contextual situation is challenging for authentication system designers. In this paper, we present a Context-driven Modelling Framework for dynamic Authentication decisions (COFRA), where the context information specifies the relevance of authentication mechanisms. COFRA is based on a precise metamodel that reveals framework abstractions and a set of constraints that specify their meaning. Therefore, it provides a language to determine the relevant authentication mechanisms (characterized by properties that ensure their appropriateness) in a given context. The framework supports the adaptive authentication system designers in the complex trade-off analysis between context information, risks and authentication mechanisms, according to usability, deployability, security, and privacy. We validate the proposed framework through case studies and extensive exchanges with authentication and modelling experts. We show that model instances describing real-world use cases and authentication approaches proposed in the literature can be instantiated validly according to our metamodel. This validation highlights the necessity, sufficiency, and soundness of our framework.