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why this is no PAI (price alignment interest) on a future contact like cleared swaps have? Am I right that you may get interest from your margin account, but you do not need to pay the interest back to your counter party.

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This blog post might help:

https://theotcspace.com/content/price-alignment-interest-pai#:~:text=PAI%20is%20the%20overnight%20cost,a%20CCP%20such%20as%20SwapClear.

Futures are settled daily, and thus considered "maturued" on each trading day. Hence, no PAI needs to be paid.

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