Last month, the Greek government said that its deficit will hit 12.7% of national income this year — the biggest in the 16-nation euro zone and twice previous forecasts from just two months ago.Above, seasonal public sector and job training program employees demonstrate in front of the Greek Parliament earlier this month, demanding measures to fight unemployment.

Worries about Europe’s weakest economies may be resurfacing after a period of relative calm.

One sign of concern: Prices are rising on so-called credit-default swaps tied to Greece, Ireland, Portugal and Italy. Investors buy these swaps, which pay off when countries default, as a kind of insurance against bad government debt.

Meanwhile, in the bond market, the “spread,” or difference, between the yield on Greek government bonds and relatively safe German debt has jumped significantly in recent days as investors have grown wary of taking on risk—especially Greek risk.

While such signals aren’t flashing as brightly as they did earlier this year, they suggest investors are worried about how Europe’s peripheral players will tackle the twin challenges of a tepid economic recovery and dire public finances in the months ahead.

“The weakest of the European Union’s membership ranks remain vulnerable to the sometimes jarring disconnect between EU economic hopes and politics on the ground,” said Scott MacDonald, director of research at boutique investment bank Aladdin Capital, in a recent note. “Investors should expect more volatility.”

Countries like Greece and Ireland are taking much of the heat.

Greek government-bond prices have been hammered lately because of concern about the country’s public finances and banks.

This month, the European Commission, the bloc’s executive arm, chastised Greece over the shoddy state of its finances, directing the government to present regular progress on improvements. Last month, the Greek government said that its deficit will hit 12.7% of national income this year — the biggest in the 16-nation euro zone and twice previous forecasts from just two months ago.

Meanwhile, credit-ratings firm Moody’s Investors Service warned the Greek and Portuguese governments last month of possible future downgrades of their government debt.

“The problem in Greece is the lack of political will to force through painful adjustments,” Aladdin’s Mr. MacDonald says.

With the year winding to a close, investors may be starting to take stock of the tough road ahead for Europe’s weakest links and each government’s relative ability to rise to the challenge. Just as they picked winners and losers among banks months ago, investors are now drawing even finer distinctions between stronger and weaker players in the euro zone.

Since Nov. 10, the cost of insuring a Greek government bond against a default for five years has jumped 22%, while the same costs for Ireland climbed 14%. Italy’s and Spain’s credit-insurance prices, meanwhile, have jumped about 18% over the same time period.

To be sure, the rising insurance costs in the derivatives market are simply another sign that investors have been wary of taking on risk in recent days. Stock markets have struggled a little, too, with the pan-European Stoxx 600 index falling 0.8% Friday to 243.62, leaving it down 1.7% last week.

Still, signs in credit markets suggest investors are turning their eyes to the expected surge of government debt that will hit the market next year as countries in Europe try to borrow their way out of the downturn without puncturing their international credibility.

“There’s no red warning light yet,” says Steve Barrow, an analyst at Standard Bank in London, in a note. “But higher [credit-default swap] prices…could prove a sign that risk is rising a bit.”