There are many methodologies described in the literature for approaching the integration process of financial markets in a given area (a comprehensive study of this subject can be found in Adam K, Jappelli T, Menichini A, Padula M, Pagano M (2002). Financists Emiris (1), Stulz (2), Ferson and Harvey (3) focus their work on the integration of capital markets. Other works look at financial integration from the angle of benefit and cost (4), from a legislative perspective (5, 6), or studying various segments of financial markets (7). In this paper, the subject of convergence is approached first of all by analysing interest rates in the Romanian interbank market, which are on a converging trend to similar values in the EU. In the second part, we propose a model for testing both the mobility of Romanian banking capitals and the European integration process of Romania’s banking sector. The model is based on the idea of maximising the Sharpe index in the portfolio theory. Furthermore, knowing that the Romanian economy and its macroeconomic variables have been a function of the American currency more than the European one, we deemed it useful to study whether and to which extent the Romanian banking sector has any converging trend to the American currency market.