We consider bilateral trade of an object between a seller and a buyer through an intermediary who aims to maximize his/her expected gains as in the previous study, in a Bayes‐Nash equilibrium framework where the seller and buyer have private, discrete valuations for the object. Using duality of linear network optimization, the intermediary's initial problem is transformed into an equivalent linear programming problem with explicit formulae of expected revenues of the seller and the expected payments of the buyer, from which the optimal mechanism is immediately obtained. Then, an extension of the same problem is considered for a risk‐averse intermediary. Through a computational analysis, we observe that the structure of the optimal mechanism is fundamentally changed by switching from risk‐neutral to risk‐averse environment.