•Correlation between returns of money market instruments in the EU and US is not stable.•Correlation rises when countries are exposed to the same external shocks.•During the last five years returns on short-term instrument have not become more interdependent.•There is no advantages in diversifications investing only in US or EU treasuries.•GARCH (2,1) turns to be more effective for time series with longer memory. This research analyse the US and the EU money markets interdependence from 2004 to 2018. The study explains to what extent the volatility of the chosen money markets instruments in two regions is inter-correlated before, during and after the financial crisis of 2008. We apply the econometric analysis and estimate time-series models of class GARCH to study the historical dynamics of interbank rates and bond returns. The study demonstrates that correlation between returns of analogous money market instruments in the EU and US is not stable over time. We find that correlation rises in periods when countries are exposed to the same external shocks as global financial crisis. Wavelet coherence analysis suggests that investors do not get any advantages of portfolio diversification investing only in US treasuries with different maturities for more than 256 days and do not get any advantages at all investing only in European bonds.