The world economy may soon find itself in the hands of a small group of bankers who must make a seemingly technical decision that has huge ramifications.

As European government leaders reached a deal early Thursday on a plan for containing the debt crisis in Greece and other nations, they looked for the owners of Greek bonds to take a significant reduction in what they are owed — as much as 50 percent. That prompts a key question: Will that officially count as a “default” for purposes of the massive market that allows investors to insure against those losses?

At issue is the market for credit default swaps, which allow investors to buy protection against an entity — whether a company or country — failing to pay its debts. If owners of Greek debt are seen as taking a voluntary cut in what they are owed, the credit default swaps would not have to pay off. If the cut is considered to be forced on debt holders, the swaps would have to pay.

In announcing the agreement, European leaders stressed that the cuts were voluntary on the part of investors. But a committee of representatives from giant banks and other financial firms will make the final call.

There are risks to the financial system either way. Having to pay off holders of credit default swaps would cause losses in financial institutions around the globe. The credit default swap market is large and opaque, which creates risks of hard-to-predict ripple effects. Following the bankruptcy of Lehman Brothers in September 2008, fears emerged over which institutions might have unknown risky exposures in the CDS market, which contributed to the global financial panic.

There were contracts insuring some $30 trillion worth of financial instruments worldwide as of the end of last year, according to the Bank for International Settlements. (The value of that insurance totals about $1.4 trillion.) Credit default swaps on Greek debt are a much smaller market, with only $3.7 billion worth of contracts guaranteeing the equivalent of $75 billion in the country’s debt.

The question is whether that market is small enough, and the financial system now resilient enough, that those contracts can be allowed to pay off without causing any broader problems.

“In theory CDS should lay off that risk widely so that the risk is diffuse and no one person stands behind it,” said M. Todd Henderson, a professor at the University of Chicago’s law school.

But there are risks to the financial system, too, if it is decided that the haircut taken by Greek bondholders is voluntary and therefore that credit default swaps do not need to pay out. If even a 50 percent decrease in the value of the bonds, undertaken after public coercion, doesn’t prompt a payout of insurance against default, it could make the CDS market less viable as a tool for companies to protect themselves against risks.

The question of whether a default has occurred is made by a committee of the International Swaps and Derivatives Association, an industry group. The “determinations committee” for Europe has representatives from 10 of the largest U.S. and European banks as voting members, including Goldman Sachs, Deutsche Bank and J.P. Morgan Chase. It also has five other giant financial institutions represented, including hedge fund D.E. Shaw and asset managers BlackRock and Pimco.

The question will likely come down to technical readings of the contracts involved, not the broader concept of whether a loss has been suffered.

“There is clearly a difference between a legal definition of default and an economic default,” said Andrew Ang, a finance professor at Columbia Business School. “This will be, if the plan goes ahead, clearly an economic default. Whether a legal default occurs is up to lawyers.”