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When we try to build a curve, we somehow need "fixings". Looks like it is when the market data created date less than the evaluation date, we put that market data into fixings. I don't really under what is this and why we need this. Could someone please give me some direction ?

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When pricing a swap with at least one floating leg referencing some index, if the fixing date of the index is before evaluation date, but the floating coupon period start date, end date, and payment date are after the evaluation date, then you need to use the realized fixing rate to calculate the coupon and discount it down from its payment date.

If you use such an instrument in the curve algorithm, then you need to carry the realized fixing rate into it (you can assume that the forward rate, expectation of index, from index tenor start date to end date - both on or after evaluation date, usually - is already known, given by index realization, unless you have good reasons to overwrite or adjust it).

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