Why Curve Construction Needs Realized Index Fixings

Summary

The document explains why realized index fixings must be supplied when building or using interest-rate curves for swaps with floating coupons. A fixing is needed when the index’s fixing date has already passed by the valuation date, even though the coupon period and payment date are still in the future. In that case, the coupon amount depends on the rate already observed in the market rather than on a forecast rate.

The realized coupon is then discounted from its payment date. The answer notes that curve-building instruments may include these periods, so the historical fixing must be carried into the calculation. For periods whose index tenor dates are still on or after the valuation date, the forward rate can generally be used as the expected index realization, unless there is a reason to adjust it. The explanation is scoped to floating-rate swap coupons and does not detail conventions for particular indices, calendars, or curve systems.

Key ideas

• A past index fixing date means the floating coupon rate has already been realized.
• Use that realized rate to calculate a coupon whose accrual and payment dates remain in the future.
• Discount the known coupon from its payment date to value it.
• Curve construction may require historical fixings when its instruments contain such coupons.
• Future index periods can generally use forward rates, subject to any justified adjustments.

Tags

# When we try to build curves, why we need fixings?


# When we try to build curves, why we need fixings?












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 ?

## Answer by ir7 (score 6, accepted)

https://quant.stackexchange.com/a/53665

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.