As the number of electric vehicles (EVs) is steadily increasing, their aggregation can offer significant storage to improve the electric system operation in many aspects. To this end, a comprehensive stochastic optimization framework is proposed in this paper for the joint operation of a fleet of EVs with a wind power producer (WPP) in a three-settlement pool-based market. An aggregator procures enough energy for the EVs based on their daily driving patterns, and schedules the stored energy to counterbalance WPP fluctuations. Different sources of uncertainty including the market prices and WPP generation are modeled through proper scenarios, and the risk is hedged by adding a risk measure to the formulation. To obtain more accurate results, the battery degradation costs are also included in the problem formulation. A detailed case study is presented based on the Iberian electricity market data as well as the technical information of three different types of EVs. The proposed approach is benchmarked against the disjoint operation of EVs and WPP. Numerical simulations demonstrate that the proposed strategy can effectively benefit EV owners and WPP by reducing the energy costs and increasing the profits.