Warping-based video stabilizers smooth camera trajectory by constraining each pixels displacement and warp stabilized frames from unstable ones accordingly. However, since the view outside the boundary is not available during warping, the resulting holes around the boundary of the stabilized frame must be discarded (i.e., cropping) to maintain visual consistency, and thus does leads to a tradeoff between stability and cropping ratio. In this paper, we make a first attempt to address this issue by proposing a new Out-of-boundary View Synthesis (OVS) method. By the nature of spatial coherence between adjacent frames and within each frame, OVS extrapolates the out-of-boundary view by aligning adjacent frames to each reference one. Technically, it first calculates the optical flow and propagates it to the outer boundary region according to the affinity, and then warps pixels accordingly. OVS can be integrated into existing warping-based stabilizers as a plug-and-play module to significantly improve the cropping ratio of the stabilized results. In addition, stability is improved because the jitter amplification effect caused by cropping and resizing is reduced. Experimental results on the NUS benchmark show that OVS can improve the performance of five representative state-of-the-art methods in terms of objective metrics and subjective visual quality. The code is publicly available at https://github.com/Annbless/OVS_Stabilization.