Building a USD One-Month LIBOR Forward Curve from Basis and Futures

Summary

The document asks how to construct a USD one-month LIBOR forward curve for pricing a one-month interest rate swap. It describes a proposed curve-building setup using one-month deposit rates at the short end, basis between one- and three-month rates, and a swap curve from the longer maturities. For the intermediate segment, it considers deriving three-month forwards from futures, with a convexity adjustment between futures rates and forward rates.

The central question is whether the quoted one-month versus three-month basis should be added to or subtracted from the futures-implied three-month forward rates to estimate one-month forwards. The document provides no resolution, worked example, market conventions, or evidence, so the appropriate sign and construction remain unanswered. The topic illustrates the need to align basis quotes, tenor conventions, and futures convexity treatment when bootstrapping a multi-tenor interest-rate curve.

Key ideas

• The curve construction combines one-month deposits, short-tenor basis quotes, futures, and longer-term swaps.
• Futures-implied rates require a convexity adjustment to represent forward rates.
• The document asks how to apply the one-month versus three-month basis to the futures-derived forwards.
• It does not give a resolved construction or specify the conventions needed to determine the basis sign.

Tags

# Constructing USD 1M Libor Forward Curve


# Constructing USD 1M Libor Forward Curve












Hope you are doing fine. I am pricing a 1month IRS. For that purpose in order tu build the forward curve i have to use the following. Since USD 1m instruments do not exist, one has to use basis between 3month and 1month

- 1 month libor rate (1month deposit rate)

- Swap Curve from 2 years using basis to build the far end of the curve.

But what about in middle part? For example BBG uses futures for the 3month forward curve. In order to get the forward rates, the formula will be the following:

Futures Rate = Forward Rates + Convexity Adjusted and Futures Rate = 1 - Futures Quotes

Since one has the basis (3m vs 1m) for the 3m,6m,9m and 1year tenor. Is it correct to add or deduct the basis spread to the 3m forward rate derived from futures to get a 1 month libor forward rate?

Thanks in advance

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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