The widespread use of distributed energy resources (DERs) in the distribution grid is changing the electricity sector worldwide in many ways. The integration of distributed renewable energy (DRE), demand response, and smart grid technologies (SGTs) can make the power systems more sustainable, efficient, and reliable. However, new entities and market mechanisms are needed to efficiently integrate those resources in the distribution grid. This paper presents a day-ahead energy and reserve market clearing and settlement model for a distribution system operator (DSO) considering the uncertainties of DRE at different nodes of the distribution grid. The problem is formulated as a stochastic optimization model, whose objective is to minimize the expected system operation cost over a specified time horizon. The problem is then solved using a Monte Carlo simulation algorithm based on sample average approximation (SAA). A case study is performed to demonstrate the effectiveness of the proposed model.