NEW YORK (TheStreet) -- As European leaders hold an emergency summit on Greece's debt crisis, one expert said there's renewed urgency to reach a deal, yet the markets have become too complacent about it.

Thanos Vamvakidis, Head of G10 FX Strategy at Bank of America Merrill Lynch, doesn't expect an agreement to be reached at today's summit, but believes the Greek government's latest proposals seem to be a step in the right direction.

Europeans will need to evaluate the proposals over the next few days before deciding whether they go far enough, the strategist said.

Vamvakidis expects there likely be another summit later this week, but said that even if there is an agreement this week, Greece might not be able to pay the International Monetary Fund by the June 30th deadline, because the logistics of releasing funds takes time.

"At least missing the payment while they have a deal is not necessarily a negative scenario because there is some flexibility. Greece will not be automatically in default to the IMF," said Vamvakidis.

But, he added, if they miss the payment without any deal in place, a series of events would occur that would lead the sovereign to default on its debt, which is why there is a sense of urgency about reaching a deal this week.

As long as they're moving toward resolution, Vamvakidis said, the European Central Bank will continue providing necessary liquidity to Greek banks, but further deals would lead to "an increased risk of a bank run in Greece."

Vamvakidis said he believes the markets are complacent and believe there will be a deal.

"The truth is, even if we see some further progress in the days ahead, too many things have to go right and the risks remain high," he said, adding that any negative developments will weigh on both European equities and the euro.

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