We introduce a dynamic network model with probabilistic link functions that depend on stochastically time-varying parameters. We adopt the widely used blockmodel framework and allow the highdimensional vector of link probabilities to be a function of a low-dimensional set of dynamic factors. The resulting dynamic factor network model is straightforward and transparent by nature. However, parameter estimation, signal extraction of the dynamic factors, and the econometric analysis generally are intricate tasks for which simulation-based methods are needed. We provide feasible and practical solutions to these challenging tasks, based on a computationally efficient importance sampling procedure to evaluate the likelihood function. A Monte Carlo study is carried out to provide evidence of how well the methods work. In an empirical study, we use the novel framework to analyze a database of significance-flags of Granger causality tests for pair-wise credit default swap spreads of 61 different banks from the United States and Europe. Based on our model, we recover two groups that we characterize as "local" and "international" banks. The credit-risk spillovers take place between banks, from the same and from different groups, but the intensities change over time as we have witnessed during the financial crisis and the sovereign debt crisis.