Before revision:  Our results show that a class of rebate barrier options can be used for this approximation , when its rebate and barrier are chosen appropriately.
After revision:  Our results show that a class of rebate barrier options can be used for this approximation . Among of them, a speci?c rebate option is also provided with a continuous rebate function, which corresponds to the unique classical solution of the associated parabolic PDE. Such a construction makes existing numerical PDE techniques applicable for its computation.