Bootstrapping a USD LIBOR Curve Beyond One Year

Summary

The document outlines market instruments used to extend a USD LIBOR curve beyond the one-year limit of cash instruments. It suggests using exchange-traded futures tied to three-month LIBOR for maturities up to five years, then using USD swap rates for longer maturities. Swap quotes represent the fixed rate exchanged against a floating leg that resets to three-month LIBOR, so they can provide inputs for building the curve even though they are not themselves LIBOR rates.

The discussion also flags an important modeling distinction: projecting LIBOR coupons and discounting cash flows may require separate curves. This is a high-level description rather than a worked bootstrapping example; it does not specify instrument conventions, calibration equations, or curve construction details. Its assumptions reflect the market context described in the answer, including the expected transition away from LIBOR, so current curve construction should use the relevant replacement benchmarks and conventions.

Key ideas

• Cash instruments provide USD LIBOR curve inputs only through one year in the described setup.
• Three-month LIBOR futures can supply curve instruments for maturities up to five years.
• Longer maturities can be supported by swap quotes, which specify a fixed rate against floating three-month LIBOR.
• Swap spreads do not prevent swap rates from serving as curve-building inputs.
• Multi-curve frameworks can use one curve to project coupons and another to discount cash flows.

Tags

# Constructing a USD LIBOR curve


# Constructing a USD LIBOR curve












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?

## Answer by Dimitri Vulis (score 4)

https://quant.stackexchange.com/a/66404

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