Euro zone finance ministers will meet on Thursday, but Greek Finance Minister Yanis Varoufakis has said that he does not plan on presenting new proposals at the meeting.
Athens faces a $1.8 billion repayment to the International Monetary Fund by the end of June and fears on a default on that bill are mounting, following comments from Prime Minister Alexis Tsipras on Tuesday, accusing Greece's lenders of trying to "humiliate" the country by imposing more cuts.
Away from Greece's own debt markets, where yields have risen sharply, the divergence of European core and periphery bond yields has been notable, with Italian and Spanish sovereign yields rising above U.S. yields for the first time since late 2014 earlier this week.
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If no agreement is reached at the emergency Eurogroup meeting, focus will shift to the European Central Bank will do with its Emergency Liquidity Assistance (ELA) to the Greek Central Bank. If that is removed, then the country faces the prospect of capital controls in Greece and possible curbs on deposit withdrawals.
All this spells bad news for bond markets, which have already seen "hardship" in recent weeks.
"We have seen a significant widening of various (credit) spreads, particularly since Monday after the breakdown and abandonment in talks over the weekend," said Peter Schaffrik, head of European economics and interest rate strategy at Royal Bank of Canada.
"I am pretty sure that as we go into Thursday's talks and into the weekends, the story is not over, so the European bond market is going to stay volatile. I think what we are seeing is the market is making room for the deal not to happen and that is why these markets have been so volatile," he said.
Spanish, Portuguese bond yields fluctuated on Wednesday ahead of the meeting having sold off sharply earlier in the week to hit multi-month highs as Greek debt contagion fears spread.
The yields on the 10-year Spanish and Italian bond traded around 2.27 and 2.25 percent respectively on Wednesday, while 10-year Portuguese bonds traded around 3.12 percent.
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Greek 10-year government paper climbed to yield over 13 percent, while short-term interest rates in Italy, Spain and Greece have also all come under heavy selling.
U.S. Treasury yields also creeped higher ahead of a closely-watched briefing from the Federal Reserve.
CEO of Principal Global Investors, James McCaughan is convinced Greece now faces default and the real question is whether the indebted country will exit from the euro currency bloc.
"Greece will default, the debt is unsustainable – I think you need a default to the official institutions because you didn't get the last time around and think that is very likely. When they default, that becomes a political issue recapitalising those institutions, not particularly a contagion issue. It is not like Lehman where the debt was all over the financial system and it was a financial shock. It is not a Lehman event, but having said that, it isn't trivial," he told CNBC.
"Then does Greece stay in the euro? That's a very interesting question – because when Greece defaults, the ECB will stop supporting the Greek banks and then you have a Cyprus position, where they are still nominally using the euro but with the capital controls," he added.