Purely financial players without any physical assets can participate in day-Ahead electricity markets as virtual bidders. They can arbitrage the price difference between day-Ahead (DA) and real-Time (RT) markets to maximize profits. Virtual bidders encounter various monetary risks and uncertainties in their decision-making due to the high volatility of the price difference. Therefore, this paper proposes a max-min two-level optimization model to derive the optimal bidding strategy of virtual bidders. In this model, the risks of uncertainties associated with the rivals' strategies and RT market prices are managed by robust optimization. The proposed max-min two-level model is turned into a single-level mixed integer linear programming model through duality theory (DT), strong duality theory (SDT), and Karush-Kuhn-Tucker (KKT) conditions. An illustrative case is designed to demonstrate the advantages of the proposed model over the deterministic model. Moreover, case studies on the IEEE 24-bus test system validate the applicability of the proposed model.