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To build a LCH swap curves, common benchmarks include cash rates, euro dollar futures and swaps. However, the euro dollar futures only exist in CME. So when you use euro dollar futures (only exist in CME) in the LCH swap curve building, are you building a LCH or CME curves?

or maybe a CME-LCH future basis should be implied from somewhere and added to the CME futures when building a LCH curve?

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