Derivatives are instruments whose values are derived from the prices of other things, like a stock or a barrel of oil or a bundle of mortgages. Originally designed to protect their holders against future risks, they evolved into vehicles that traders used for financial speculation. Unlike stocks, they often aren’t traded over public exchanges, which means the market — and who is exposed to what — is opaque.

“It’s a global market, so you really have to have a global set of data,” said Werner Bijkerk, the former head of research at the International Organization of Securities Commissions, an umbrella group for regulators around the world overseeing derivatives markets. “You can start running ‘stress tests’ and see where the weaknesses are. With this kind of patchwork, you will never be able to see that.”

A decade after a financial crisis fueled in part by a tangled web of derivatives, regulators still have an incomplete picture of who holds what in this $600 trillion market.

United States regulators, however, get detailed information only about the derivatives traded by Goldman Sachs International. Thanks to a loophole in laws enacted in response to the financial crisis, trades by Goldman Sachs International Bank don’t have to be reported.

Both trade financial instruments known as derivatives with hedge funds, insurers, governments and other clients.

In the maze of subsidiaries that make up Goldman Sachs Group , two in London have nearly identical names: Goldman Sachs International and Goldman Sachs International Bank.

The 2010 Dodd-Frank law was supposed to improve regulators’ ability to monitor derivatives. American banks had to start reporting specifics about their trades, including whom they traded with, to the Commodity Futures Trading Commission.

The goal was to prevent a recurrence of the financial crisis, when fatal problems at Lehman Brothers caused a tidal wave of troubles at other banks that were connected through derivatives. In part because nobody could map out those connections, nobody knew where problems lurked, and fearful banks stopped lending to one another.

But the Dodd-Frank Act contained a big gap: Banks don’t have to disclose to American regulators their holdings of derivatives housed in certain offshore entities. The critical variable is whether the American parent company is legally on the hook to bail out its foreign subsidiary if it gets into trouble. As long as the answer is no, the foreign entity isn’t subject to the Dodd-Frank requirements.

The size and severity of this blind spot are hard to measure. One consequence is that United States regulators are unable to grasp the full exposure of American banks to their foreign rivals. Germany’s troubled Deutsche Bank, for example, is one of the largest players in the derivatives market, and much of its derivatives trading occurs in foreign markets that are outside the purview of American regulators. That means they have limited visibility into United States banks’ connections to Deutsche Bank.

Other countries’ regulators can seek information about those holdings, but they generally do not collect the same data that is reported to American regulators.

The Dodd-Frank law “didn’t really give a mandate to coordinate on the things that naturally would benefit most from coordination, one of which is the flow of information,” said Guy Dempsey, a derivatives lawyer.

Goldman, for example, reports its total exposure to the derivatives market as a single number: The bank had $45 billion in over-the-counter derivatives alone on its balance sheet at the end of 2017. Because of the trading in its Goldman Sachs International Bank unit and other foreign subsidiaries, a certain amount of those trades are invisible to American regulators.

A Goldman spokesman said less than 1 percent of the bank’s global derivatives activity wasn’t visible to the Commodity Futures Trading Commission, but he declined to comment further.

For JPMorgan Chase, trades not reported to the commission account for less than 10 percent of all the bank’s derivatives, a spokesman said. (The firm reported $56.5 billion in outstanding derivatives for 2017.)

A Citigroup spokeswoman said the bank’s European derivatives trades were made “predominantly” through subsidiaries that reported their trades to the Commodity Futures Trading Commission.

The portion of Bank of America’s derivatives portfolio that isn’t reported to regulators is not discernible in its public filings. A bank spokesman would say only that the percentage is small. A Morgan Stanley spokesman said “virtually all” of its trades were reported to American regulators.

The banks say that they aren’t trying to hide anything and that in some cases they are responding to demands from overseas clients who don’t want the United States government looking at their transactions. Even foreign bank regulators argue there’s no reason American law should apply to financial instruments held outside the United States.

“This problem, I think, is really driven more by regulators each wanting their own silo,” said Sheila Bair, a former chairwoman of the Federal Deposit Insurance Corporation. “I think the industry would be fine with some type of consolidated reporting.”

Mr. Dempsey, the lawyer, said, “What you have is a picture that has more clarity to it than what the regulators had in 2008, but you still don’t have maximum clarity.”

Regulators can still monitor risk for individual institutions. The Federal Reserve, for example, can ask for specific information about derivatives trades as it sees fit. But because the trades aren’t automatically reported, the regulator would have to decide which trades to ask about beforehand. Theoretically, the Fed could ask for banks to report every single trade, but the central bank hasn’t done that.

In October 2016, the Commodity Futures Trading Commission proposed a rule that would have closed the reporting loophole by requiring all American bank subsidiaries to report their derivatives exposure. It also would have subjected the subsidiaries to financial regulations that would have made derivatives trading less profitable.

The banking industry opposed the rule. After President Trump took office, it was never authorized.

Officials at the Commodity Futures Trading Commission acknowledge that there is a problem. The agency noted in an April paper that the current reporting “cannot provide regulators with a complete and accurate picture” of risks in the market.

Even so, Amir Zaidi, the director of the commission’s market oversight division, said more data was available to regulators now than before the financial crisis, enough to enable “effective oversight.”

In a recent paper, a University of Maryland law professor, Michael Greenberger, argued that banks were exploiting the disclosure loophole and creating a major vulnerability for the financial system.

The largest banks “have engineered a way to evade Dodd-Frank’s regulations at will,” Mr. Greenberger wrote. He warned that in a period of financial stress, derivatives cause cascading losses. Because the ownership and connections of those derivatives remain murky, he wrote, “the economic chaos and harm of the 2008 financial meltdown may very well be repeated.”

Mr. Greenberger’s warnings — published last month by the Institute for New Economic Thinking, a progressive think tank — have been endorsed by the former Federal Reserve chairman Paul Volcker and Thomas M. Hoenig, who stepped down as vice chairman of the Federal Deposit Insurance Corporation in April.

Mr. Hoenig noted that the universe of derivatives was already very complicated, “and so when you make it even more opaque in a foreign subsidiary, I think the ability to control outcomes is very different.”

He recalled earlier efforts to bring transparency to the derivatives markets. Such proposals were derailed by senior officials in the Clinton administration, and Mr. Hoenig warned against repeating that mistake.

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