We employ a two-stage general dynamic factor model to analyze co-movements between returns and between volatilities of stocks from the U.S., European, and Japanese financial markets. We find two common shocks driving the dynamics of volatilities—one global shock and one United States–European shock—and four local shocks driving returns, but no global one. Co-movements in returns and volatilities increased considerably in the period 2007–2012 associated with the Great Financial Crisis and the European Sovereign Debt Crisis. We interpret this finding as the sign of a surge, during crises, of interdependencies across markets, as opposed to contagion. Finally, we introduce a new method for structural analysis in general dynamic factor models which is applied to the identification of volatility shocks via natural timing assumptions. The global shock has homogeneous dynamic effects within each individual market but more heterogeneous effects across them, and is useful for predicting aggregate realized volatilities.