Building a Basis-Adjusted Six-Month LIBOR Forward Curve

Summary

The discussion explains how a six-month LIBOR forward rate can be derived from a three-month reference curve when valuing a fixed-for-floating interest rate swap. First, a three-month LIBOR curve is constructed from market instruments such as futures and swaps. The difference between three-month and six-month forward rates is then inferred from traded tenor basis swaps, which quote the market spread between the two tenors.

That implied basis spread is added to the three-month forward rate to obtain a six-month forward. The answer describes calibration to two market references: shorter maturities are guided mainly by three-month versus six-month basis swaps, while longer maturities are also aligned with six-month LIBOR swaps. This is a high-level curve-building explanation, not a complete pricing recipe; it gives no interpolation, bootstrapping, conventions, or numerical example. It also refers to LIBOR curves, so the approach should be read in that historical benchmark context rather than as a specification for current replacement benchmarks.

Key ideas

• Construct the three-month LIBOR curve from relevant futures and swap instruments.
• Use traded three-month versus six-month tenor basis swaps to infer the tenor spread.
• Add the implied basis spread to the three-month forward to derive the six-month forward.
• Use shorter tenor basis quotes and longer six-month swap quotes to guide different curve regions.

Tags

# How to compute for basis adjusted forward rate?


# How to compute for basis adjusted forward rate?












To give you a brief background, I'm valuing a fixed-for-float Interest Rate Swap (IRS) using Bloomberg. I put in a notional amount in (USD) and a assigned 6MO USD LIBOR as the reference index for the floating leg. I want to know how Bloomberg computed for the floating rates it used to compute for the floating cash flows and they told me that: 6MO USD LIBOR forward rate is computed using 3MO USD Swap curve then they did a basis adjustment to come up with basis adjusted forward rate. I would like to know how to compute for this basis adjusted forward rate? Thank you.

## Answer by rip (score 0)

https://quant.stackexchange.com/a/43167

First a 3M Libor curve is built (using futures and 3M Libor swaps) and then they try to compute the adequate spread implied in the market between 3M and 6M LIBOR forwards.

For calculating this spread, they use tenor basis swaps like 3M-6M LIBOR basis swaps traded in the market. The 6M LIBOR is such that:

1) it's spread with 3M LIBOR matches the observed spread between 3M Libor forward and 6M Libor forward in 3-6M tenor basis swaps (traded OTC). This is mostly for shorter end of the curve.

2) The 6M forward obtained matches the 6M LIBOR swaps traded in the market. This is for the longer end of the curve.

Apply the implied spread on top of the 3M LIBOR forward rate to get the 6M LIBOR .

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.