The swap contracts, mostly underwritten by Lehman Brothers, were intended to hedge interest rate risks on about $650 million in bonds issued by the Giants entity.
When the swaps were terminated in September 2008, at a time Lehman filed for bankruptcy, Giants Stadium "undertook a contorted plan" to avoid paying millions of dollars, the investment bank said in a lawsuit on Wednesday.
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Giants Stadium estimated that Lehman owed it about $301 million after the termination of the swaps contracts, a figure disputed by Lehman, the filing said.
Later, Boston-based Baupost Group, one of the world's biggest hedge funds, bought the Giants Stadium claims against the Lehman estate and in turn sought to amend its claims to about $585 million for each contract, the lawsuit said.
Lehman said the swaps were about $60 million in its favor just days before it filed for Chapter 11.
On Wednesday, Lehman sought damages of no less than $94 million plus interest, after what is says was the "proper calculation" of the settlement amount of the swaps.
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Giants Stadium has an ownership interest in 50 percent of the MetLife stadium, while the other half of the stadium is held by the owners of New York Jets.
Lehman emerged from bankruptcy last year with a liquidation plan slated to repay creditors about $65 billion, or an average of about 21 cents on the dollar for allowed claims. The winding down is expected to take a few years.
The case is Lehman Brothers Holdings vs Giants Stadium LLC, Case No. 13-01554, U.S. Bankruptcy Court, Southern District of New York.