In this paper, we propose a two-step approach for conducting statistical inference in financial networks of volatility, applied to a network of European sovereign debt markets. The static results highlight that, contrarily to the intuition, southern European bonds exhibiting most volatility during the European debt crisis were not necessarily net transmitters to the network. We also find that the best monetary and macroprudential policy stances to achieve low volatility transmission are to target low inflation and low financial stress. The dynamics of the model show that the central bank should adjust which variable targets depending on the time period.