This paper proposes a portfolio choice model with two countries to evaluate the specific role of volatility and co-volatility risks in the formation of long-term European interest rates over the crisis and post-crisis periods with an active role of the European Central Bank. Long-term equilibrium rates depend crucially on the covariances between international bond yields anticipated by investors. Positively anticipated covariances amplify the phenomena of fundamental contagions related to the degradations of public finance and solvency of sovereign debt issuer, while negatively anticipated covariances amplify the phenomena of Flight-to-quality. The two-step econometric approach over the period January 2006 to September 2016 analyses 21 European market pairs in a bivariate GARCH framework. Empirical results show that the decline in German and French long-term rates from March 2011 is partially due to the decrease in both risk premium and covariances with periphery countries. These declines actually amplify the mechanisms of Flight-to-quality. Finally, a lower sensitivity of rate to volatility and co-volatility risks during the crisis period gives credit to the hypothesis of a occasional fragmentation of the European sovereign bond markets