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After finally launching it's highly anticipated QE program, the European Central Bank now faces another major task: dealing with Greece.
If the pre-polls for Sunday's elections are correct, the next Prime Minister of Greece will likely be Alexis Tsipras, leader of the radical-left Syriza party. Tsipras' economic advisors say one of their first missions will be to renegotiate the debt Greece owes to the ECB—an explosive idea in both political and central banking circles.
"There are are some red-lines that will simply be non-negotiable, for the ECB in particular," said Doug Rediker of International Capital Strategies, who was formerly the U.S. representative to the International Monetary Fund (IMF).
Syriza remains undeterred. "Our party's mandate is to renegotiate," said Yanis Varoufakis, who is tipped by some to be Syriza's new finance minister.
Varoufakis, who was most recently an economics professor at the University of Texas in Austin and describes himself as a libertarian Marxist, argued that there was no hope of Greece paying back all that it owes.
"Greece went bankrupt in 2010 and what did Europe do in its infinite wisdom? It tried to deal with a solvency problem by extending the largest loan in history on the weak shoulders of the bankrupted Greek state."
Greece certainly has a mountain of debt, owing more than $350 billion, not just to the European Central Bank (ECB) but also to the IMF, other European governments, and private investors.
To the ECB specifically, Greece owes 27 billion euros ($30 billion), in the form of bonds bought by the central bank on the open market back in 2010 and 2011, at the height of the European financial crisis. Under former ECB President Jean Claude Trichet, Mario Draghi's predecessor, the central bank bought the bonds in an effort to lower Greece's interest rates so it could borrow again at an affordable rate from the capital markets.
Now, many of those bonds are coming due. Greece has a principal repayment of 3.5 billion euros in July and another 3 billion euros in August.
Syriza's economic policy team wants the ECB to dramatically ease Greece's repayment terms. When CNBC spoke with several members of Syriza, it was clear this this was a top priority—and could lead to a showdown between the leftists and the central bank.
"The ECB can do a lot of things," said John Milios, a self-described Marxist with a PhD in economics. "One solution could be a swap."
In exchange for the bonds currently held by the ECB, Milios wants to give the central bank a different type of bond—a "zero-coupon perpetual." In other words, a bond that pays a zero interest rate for the entire duration of the bond, which in this case, would be forever.
In the restructuring world, zero coupon perpetuals are snarkily referred to as "wallpaper."
But Milios insists the ECB would eventually get paid back. The country would begin buying back the debt, i.e. repaying it, once the economy has grown sufficiently that the country's debt-to-GDP ratio falls to 20 percent, from the current level of 174 percent.
Milios calculates this would take 58 years. He's written a paper, available here, in which he suggested that his suggested policy for Greece should take place in all of the highly indebted euro zone countries.
Varoufakis suggested a slightly different variation on Milios' plan. He too wanted the ECB to accept a zero-coupon perpetual, but one with GDP warrants attached. These are payments a debtholder receives that are tied to a country's GDP growth, and have been used in sovereign debt restructurings in the past. The holder of the warrants gets paid when the economy grows.
What does the ECB think of these ideas? That's unknown as yet, as a spokesperson for the central bank declined to comment on anything related to Greece until after the results of the elections were known.
But the suggestion that a Syriza government may not want to pay back the ECB on time puts Greece in a tenuous position when it comes to the central bank's newly announced quantitative easing program.
During last Thursday's press conference, Mario Draghi said: "There are obviously some conditions before we can buy Greek bonds."
Read MoreECB stimulus may ease Greek concerns
Greek bonds will be excluded from the new program until at least July, Draghi explained, because the bank already owns so much Greek debt that it exceeds ownership limits. Draghi implied however that once Greece pays back the bonds due in July, the country's debt will become eligible for the program.
However, Draghi also said the country must be in compliance with the bailout program imposed by the IMF and the European Commission on the country—a program that Tsipras has also promised to renegotiate.
Syriza risks overplaying its hand, said International Capital Strategies' Rediker. "Given that the ECB controls the liquidity of the Greek banking system, and also serves as its regulator through the SSM (Single Supervisory Mechanism), going toe-to-toe with the ECB is one battle that could end very badly for the Greek government."
If the ECB were to stop funding the liquidity of the Greek banks, the banks could collapse—an event that could lead to Greece abandoning the euro and printing its own money once more.
Milios didn't believe it would come to that, saying, "No one wants a collapse of banks in the euro zone. This is going to be Lehman squared or to the tenth. No one wants to jeopardize the future of the euro zone."
Meanwhile, the Syriza team's plans don't stop with the ECB. Syriza wants a writedown of the nearly 200 billion euros in loans from the European Financial Stability Fund and other European governments that Greece has received.
However, the European Commission has long said that a writedown is out of the question—although lower interest rates and longer maturities are a possibility, as long as Greece sticks to the terms of its bailout program.
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