Modern market management systems continue to evolve due to the intentions to improve system security and reliability. This evolvement has been leading to a transition of market auction models from a deterministic structure with approximations on the reliability criteria (e.g., acquirement of contingency reserve through proxy reserve policies) to explicit representation of contingencies (e.g., estimation of post-contingency states via participation factors and stochastic programming). This paper proposes a comprehensive framework to establish various procedures for evaluating: (i) transparency and incentive compatibility of different contingency modeling approaches, and (ii) efficiency of two possible stochastic market designs. First, the concept of securitized LMP is presented to solve the issue of how market participants should be compensated for providing N-1 reliability services. Then, pricing implications and settlements of three market models are compared: (i) a deterministic market model with proxy serve policies, (ii) state-of-the-art market models with estimated post-contingency states, and (iii) a two-stage stochastic market model. Second, this paper evaluates two stochastic market models while accounting for potential adjustments from day-ahead scheduling to real-time operation: (i) minimizing expected operating cost of all N-1 scenarios, and (ii) minimizing the base-case (or no contingency) cost. These analyses are conducted on IEEE 118-bus test system.