We utilize the cross-quantilogram method to assess the predictive capacity of geopolitical risk (GPR) on volatility spillovers calculated by the time-varying parameter vector autoregressive model, across international commodity, exchange, and U.S. and Chinese stock markets. The findings yield three notable observations: First, we establish the directional predictive influence of GPR on net and net pairwise volatility spillovers, indicating discernible shifts in the risk roles of specific markets and transmission pathways. Second, these shifts, anticipated by GPR, manifest swiftly within a single day and subside within a quarter, albeit with varying durations contingent on market categories and transmission pathways. Third, disparities are evident in the predictive effectiveness of geopolitical acts and geopolitical threats. These findings remain robust even when considering factors such as economic policy uncertainty, alternative proxies, and other spillover models. •We study predictive power of geopolitical risk for cross-market volatility spillovers.•Geopolitical risk has the capacity to forecast the direction of spillovers.•The Network structure changes subsequent to GPR intensification.•GPT’s predictive ability differs from GPA’s, resembling GPR’s more closely.