In this paper, through jointly considering the interference caused to the primary user (PU) from one pair of secondary transceivers, the optimal power allocation is studied for the underlay cognitive two way network. Under the quality of service constraint of the PU transmission, two different objective functions are considered for the SUs to maximize the sum achievable rate or maximize the minimal achievable rate. The optimal closed-form power allocations are achieved for both scenarios. The effectiveness of our proposed schemes is verified through simulations.