Traditional frameworks for risk assessment do not work well for cloud computing. While recent work has often focussed on the risks faced by firms adopting or selecting cloud services, there has been little research on how cloud providers might assess their own services. In this paper, we use an in-depth review of the extant literature to highlight the weaknesses of traditional risk assessment frameworks for this task. Using examples, we then describe a new risk assessment model (CSCCRA) and compare this against three established approaches. For each approach, we consider its goals, the risk assessment process, decisions, the scope of the assessment and the way in which risk is conceptualised. This evaluation points to the need for dynamic models specifically designed to evaluate cloud risk. Our suggestions for future research are aimed at improving the identification, assessment, and mitigation of inter-dependent cloud risks inherent in a defined supply chain.