We present new formulations of the stochastic electricity market clearing problem based on the principles of stochastic programming. Previous analyses have established that the canonical stochastic programming model effectively captures the relationship between the day-ahead and real-time dispatch and prices. The resulting quantities exhibit desirable guarantees of revenue adequacy, cost recovery, and price distortion in expectation. Motivated by these results, we develop alternative stochastic programming model formulations that differ in how we model the nonanticipativity requirement. We design new pricing mechanisms by developing suitable dual optimization problems for these models. We analyze these pricing mechanisms to assess their ability to provide revenue adequacy for the system operators, cost recovery for generators, and price distortion. Unlike the previous mechanisms that yield the desired properties in expectation, one of our pricing mechanisms extends the benefits of cost recovery and bounded price distortion under every scenario while retaining the long-run revenue adequacy for the system operator. We demonstrate these benefits through numerical experiments conducted on well-known test systems.