Speaking to the Financial Times, Michael Wolf, chief executive of the institution, explained that supporting the countries now would avoid the problems that could arise if they were left to fend for themselves.
He said: "The EU would definitely like [the Baltic countries] to succeed. In relative terms, supporting these countries is not very costly."
Although Swedbank, which is the largest lender in the Baltic region, has just announced its second rights issue in a year, Mr Wolf is confident that things are stabilising in Latvia, Estonia and Lithuania.
The latest rights issue raised 15 billion Swedish kroner and was underwritten by existing shareholders, Bank of America-Merrill Lynch and Credit Suisse.
Recently, Bloomsburg reported that Swedbank was asked by Latvia to increase the amount it lends in the nation.
Around 40 per cent of Latvians are customers of the institution.
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