Three of the nation's biggest banks are competing to run the back office for Fi-Trac, an interbank bond trading service that Fidelity Investments is marketing, according to a source close to the negotiations.

Manufacturers Hanover, Security Pacific Corp., and Bankers Trust are vying for a role in the product, which is being pitched to bank treasurers who now rely on Wall Street to execute government bond trades.

The electronic trading system, which is designed to handle all fixed-income products and equities, needs at least one bank to match and settle trades.

Its role would be to ensure that the buyers' funds move to sellers.

Each of the contending banks already does a big business in settlement and clearing and works with Fidelity. However, the source said that Chase Manhattan Corp. - another big player - declined to bid.

The contract is expected to be large, though fees will depend on volume.

Trading experts handicapping the system expect it to be a success, despite opposition from the Wall Street middlemen who currently broker the trades.

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