The chief of French bank Societe General said further European bank stress tests aren't needed as their exposure to sovereign debt is known.

"The exposure to sovereign debts is public. They are well known," Societe General CEO Frederic Oudea told CNBC on Tuesday, according to the channel's website.

"Markets can make calculations and I think generally speaking, people totally overestimate the impact of any kind of scenario on this sovereign debt."

The stringency of the European bank stress tests carried out in July has been called into question by the markets after Bank of Ireland and Allied Irish Banks passed only to need bailouts a few months later.

Of 91 European banks tested last July, only seven — five in Spain, one in Germany and one in Greece — were found to be vulnerable to economic stress.

EU economic affairs commissioner Olli Rehn said earlier this month new "even more rigorous and even more comprehensive" stress tests would be organized in February, this time including a look at liquidity positions.

The president of the European Central Bank, Jean-Claude Trichet, also said earlier this month that bank stress tests were "useful" and would be organized regularly in the European Union.

Although Oudea felt further bank stress tests weren't needed, he said fears of contagion in the eurozone over deficit and debt problems could make for another year of volatility on the markets.

Nevertheless, Oudea said that fears of contagion had been overblown.

He added if European governments are able to come to a solution, it could "make the volatility disappear."

Analysts and markets were underwhelmed by the European summit earlier in December, where leaders decided to move to establish a permanent rescue fund, but didn't decide on its size and did not provide any details on potentially forcing investors to suffer losses in future bailouts.