This paper proposes a stochastic optimization model for generating the optimal price-maker trading strategy for a wind power producer using virtual bidding, which is a kind of financial tool available in most electricity markets of the United States. In the proposed model, virtual bidding is used to improve the wind power producer’s market power in the day-ahead (DA) market by trading at multiple buses, which are not limited to the locations of the wind units. The optimal joint wind power and virtual trading strategy is generated by solving a bi-level nonlinear stochastic optimization model. The upper-level problem maximizes the total expected profit of the wind power and virtual bidding while using the conditional value at risk (CVaR) for risk management. The lower-level problem represents the clearing process of the DA market. By using the Karush-Kuhn-Tucker (KKT) conditions, duality theory, and big-M method, the bi-level nonlinear stochastic model is firstly transferred into an equivalent single-level stochastic mathematical program with the equilibrium constraints (MPEC) model and then a mixed-integer linear programming (MILP) model, which can be solved by existing commercial solvers. To reduce the computational cost of solving the proposed stochastic optimization model for large systems, a method of reducing the number of buses considered for virtual bidding is proposed to simplify the stochastic MPEC model by reducing its decision variables and constraints related to virtual bidding. Case studies are performed to show the effectiveness of the proposed model and the method of reducing the number of buses considered for virtual bidding. The impacts of the transmission limits, wind unit location, risk aversion parameters, wind power volatility, and wind and virtual capacities on the price-maker trading strategy are also studied through case studies.