  In this paper, we propose a methodology based on piece-wise homogeneous
Markov chain for credit ratings and a multivariate model of the credit spreads
to evaluate the financial risk in European Union (EU). Two main aspects are
considered: how the financial risk is distributed among the European countries
and how large is the value of the total risk. The first aspect is evaluated by
means of the expected value of a dynamic entropy measure. The second one is
solved by computing the evolution of the total credit spread over time.
Moreover, the covariance between countries' total spread allows understand any
contagions in EU. The methodology is applied to real data of 24 countries for
the three major agencies: Moody's, Standard and Poor's, and Fitch. Obtained
results suggest that both the financial risk inequality and the value of the
total risk increase over time at a different rate depending on the rating
agency and that the dependence structure is characterized by a strong
correlation between most of European countries.
