USD_LIBOR rates are only published up to 12 months.

how would you approach constructing the curve to at least a 30-year tenor, to price for example an interest rate swap.

I have heard that swaps can be used, however, I am not sure how this would be done. Nowhere are there real live examples. Most websites just mention that you can use swap rates. but how?

My approach:

Use USD LIBOR up to 12 months, add US Swap rates for 1 year +

But if I am correct, Swap rates are not equal to LIBOR rates, as they say, that the difference is the 'swap spread'.

so how can we use these US swap rates, to construct the USD LIBOR curve beyond 12 months?

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    $\begingroup$ I tried to answer a similar question here: let me know if that helps. $\endgroup$ Aug 11 at 12:20

Indeed, cash instruments go out to 12 months. Beyond 12 months, you can use swap rates, as you said, but up to 5 years you're better off using quotes for exchange-traded futures whose underlying is 3mo libor; and use swap rates after 5 years.

As of this writing, USD swap rates are quotes for swaps where one leg is fixed and another leg resets from 3mo Libor. The quote is the rate of the fixed leg. All this likely to change in a few years as LIBOR goes away.

Also these days you are likely to need a multi-curve, i.e. you'd use LIBOR for projecting coupons, but somehting else for discounting.

I suggest you read this paper: Ametrano, Bianchetti, Everything You Always Wanted to Know About Multiple Interest Rate Curve Bootstrapping but Were Afraid to Ask (2013) https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2219548

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    $\begingroup$ Just one thing to add in my opinion; usually you don't mix libor tenors in curve construction. If your swap is against 3m libor, you wouldn't use 6m, 12m etc but futures or FRAs for anything not associated with the tenor in the swap (plus swaps quotes for long end). $\endgroup$
    – AKdemy
    Aug 11 at 12:43
  • $\begingroup$ Thank you @AKdemy! Yes indeed. @Michelle Conversely, if you're going to use your curve for basis swaps (e.g. 2 floating leg, 3Mo v 6o libor) then you'll need quotes for such swaps. And if you're using futures, then you should include convexity adjustments. Lots of other details that are likely to change as we switch to SOFR. I think Ametrano and Bianchetti is a good tutorial for someone leanining from scratch, but there are other resources, e.g. you might find walking through FinancePy helpful. $\endgroup$ Aug 11 at 13:15

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