Recently, several pari-mutuel mechanisms have been introduced to organize prediction markets, such as the logarithmic scoring rule, the cost function formulation, and sequential convex pari-mutuel mechanism (SCPM). In this work, we develop a unified framework that bridges these seemingly unrelated models for centrally organizing contingent-claim markets. Our framework establishes necessary and sufficient conditions for designing mechanisms with many desirable properties such as proper scoring, truthful bidding (in a myopic sense), efficient computation, controllable risk-measure, and guarantees on the worst-case loss. As a result, we develop the very first proper, truthful, risk-controlled, loss-bounded, and polynomial-time scoring rule, which neither of the previous proposed mechanisms possesses simultaneously. Thus, in addition to providing a general framework that unifies and explains all the existing mechanisms, our work would be an effective and instrumental tool in designing new market mechanisms. We also discuss applications of our framework to general open markets for dynamic resource pricing and allocation. This is a joint work with Shipra Agrawal, Erick Delage, Mark Peters, Anthony So, and Zizhuo Wang.