Abstract A spatiotemporal approach is proposed for modeling risk spillovers using time-varying proximity matrices based on observable financial networks and a new bilateral Multivariate GARCH specification is introduced. The covariance stationarity and identification of the model is studied, developing the quasi-maximum-likelihood estimator and analysing its consistency and asymptotic normality. Further, it is shown how to isolate risk channels and it is discussed how to compute target exposure in order to reduce the system variance. An empirical analysis on Euro-area sovereign credit default swap data indicates that Italy and Ireland are key players in spreading risk, France and Portugal are major risk receivers, and Spain’s non-trivial role as a risk middleman is uncovered.