By Bradley Hope, Emily Glazer and Christopher M. Matthews 

Credit Suisse Group AG and Barclays PLC, two of the biggest operators of "dark pools," have entered settlement negotiations with the New York attorney general and the Securities and Exchange Commission over allegations of wrongdoing in the private trading venues, said people familiar with the matter.

Credit Suisse is in talks to pay a fine in the high tens of millions, which would be the largest fine ever levied against an operator of a private trading venue, and the Barclays discussions also suggest a large fine, the people said.

Deals with the banks could come as soon as the next several weeks, though talks could still fall apart, they said.

Representatives of Credit Suisse and Barclays declined to comment.

Dark pools, which allow buyers and sellers to swap shares with greater anonymity than they can on the stock market, have come under scrutiny from regulators in the past several years, and enforcement activity has been heating up lately.

Analysts say that while the pending settlements could lead to tighter regulation of off-exchange trading, they are unlikely reduce the amount of dark-pool trading.

Dark pools, along with so-called internalizers who execute trades on behalf of retail brokers, account for nearly 40% of all stock trading, according to the market-research firm Tabb Group LLC.

"This may serve to finally sterilize dark pools," said Larry Tabb, chief executive of Tabb Group, referring to the likelihood that operators disclose more information about trading activity and stay in compliance.

The size of fines against dark-pool operators is on the rise.

Investment Technology Group Inc., a New York brokerage, said last month it had set aside $20.3 million to settle allegations of wrongdoing related to its dark pool, Posit, with the SEC.

The largest case before that was against UBS Group AG, which in January agreed to pay $14 million to settle allegations with the SEC it created an uneven playing field inside its dark pool.

Credit Suisse operates the largest dark pool in the U.S. Called CrossFinder, it matched more than 430 million shares during the week beginning July 20, according to data from the Financial Industry Regulatory Authority.

The case against Credit Suisse includes allegations that it provided unfair advantages to some traders, violated rules against pricing of stocks and didn't adequately disclose to investors how CrossFinder works, according to the people familiar with the matter.

Regulators also are scrutinizing Credit Suisse's system of auctioning the right to trade against retail stock-market orders to trading firms in the dark pool.

The setup resembled a waterfall, said people familiar with the matter, in that the first firm to trade against the flow would pay one price and subsequent auctions to other traders would go down in price.

Barclays was accused by the New York attorney general in July 2014 of lying to clients about the extent of high-speed trading in its dark pool.

In one example in the lawsuit, a Barclays executive allegedly instructed two employees to mislead a large institutional investor about how much of its trading was done in the dark pool and how often those trades were with high-frequency firms.

When one of the employees provided the accurate information to the investor anyway, the employee was fired, according to the suit.

Barclays has denied it defrauded customers and fought to have the case dismissed. The civil case, filed in New York State Supreme Court, is ongoing.

Institutions, including hedge funds and large mutual funds, use dark pools to buy and sell stock without having a large impact on the price. If a firm is trying to make a purchase of 100,000 shares, it is preferable to try to find another large institution looking to sell rather than take it directly to the stock market.

"Investors believe there is value to trading in the dark," said Alex Green, president of the consultancy FuturePoint Advisors LLC and a former head trader at hedge funds. "The regulators are exposing some of the things that have gone on, but there will still be a demand to trade in dark pools."

Most orders on stock exchanges, for instance, are publicly displayed to all other investors in the form of a bid or an offer. The institution's name isn't given, but their buying or selling intent is broadcast to others.

In a dark pool, a firm's bid or offer also is anonymous and is only executed if another firm puts in a matching order.

However, over the years dark pools have become more complicated and included facilities for a broader swath of traders to access the venues. Regulators have been probing a range of firms on whether they adequately disclosed the rules of trading to participants and whether any traders--including high-frequency traders--were given advantages over others.

Deutsche Bank AG, Morgan Stanley and Goldman Sachs Group Inc. also have been investigated by the New York attorney general. The banks declined to comment.

Jean Eaglesham contributed to this article.

Write to Bradley Hope at bradley.hope@wsj.com, Emily Glazer at emily.glazer@wsj.com and Jean Eaglesham at jean.eaglesham@wsj.com

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