This paper proposes a new wind offering strategy in which a wind power producer employs demand response (DR) to cope with the power production uncertainty and market violations. To this end, the wind power producer sets demand response (DR) contracts with a DR aggregator. The DR aggregator behavior is modeled through a revenue function. In this way the aggregator aims to maximize its revenue through trading DR with the wind power producer, other market players and the day-ahead market. The problem is formulated in bilevel programming in which the upper level represents wind power producer decisions and the lower level models the DR aggregator behavior. The given bilevel problem is then transformed into a single-level mathematical program with equilibrium constraints (MPEC) and linearized using proper techniques. The feasibility of the given strategy is assessed on a case of the Nordic market.