# Properly interpreting LIBOR curves?

I have a confusion regarding LIBOR curves. I understand what LIBOR means, but what exactly is meant by a LIBOR curve? I would imagine a curve where on the x-axis is time and y-axis the 6-month LIBOR so basically the LIBOR 6M curve is the forward curve, i.e what we think the 6m LIBOR will be on a future date from now.

Now looking into the data I have, it gives me the 6-month LIBOR for a set of tenors (say 1 up to 1300). How do I interpret these numbers? It looks like a yield curve, but I don't know what exactly is meant by, say a 10-day maturity for 6M-LIBOR? Can someone provide me with a clear example?

Thanks!

• Did you find an answer to your question? Could you share it, please? I don't understand what is represented by maturities less than the tenor of the index, e.g. maturities of ON, 1W, 2W, etc for 6M LIBOR curve. Thank you Oct 16 '20 at 12:23

Interest rate derivative trading relies on curves. The LIBOR rate, be it 1month, 3month, 6month etc is published and determined every day but derivative contracts continue to speculate on what futures day's LIBOR publications will be.

A 6M Libor curve does one thing and one thing only. It estimates what 6M Libor will be on any future date. I.e you can 'interrogate' the curve to tell you the 6M Libor estimate for 10th Sep 2019 or 23 June 2049.

The curves 1M, 3M, 6M, 12M etc, are derived not by specific knowledge of any of those specific days, but by some known market prices, e.g. the 10Y IR Swap rate and then a non-linear solver derives the best estimate of smooth, interpolated curves that matches the known market prices for those instruments the best.

• So, taking the last sentence from the OP, what is represented by "a 10-day maturity for 6M-LIBOR"? I would have expected that the first maturity point on a yield curve should be the tenor, e.g. 6M maturity for 6M LIBOR. Thank you Nov 27 '20 at 16:20
• 10-day matuity for 6M libor is probably referring to what the 6M LIBOR rate will be published as in 10 days time. ALthough the current 6M-Libor is a good datapoint that is probably used in the construction it is not always relevant, for example if the FED has raised funding rates on the day since the last LIBOR publication, for example.
– Attack68
Nov 29 '20 at 20:26

The Libor 6Month refers to the Plain Vanilla Swaps paying 6 Month Libor on the floating Leg and Fixed on ther other.

• With that being said, the points on the yield curve are Par Swaps rates from the Fixed leg of the Swap, which are then bootstrapped.
• If you consider the 6 Month Libor index as the first point in your curve, you can then obtain the rest of the tenors by just applying the 3MLibor-6MLibor basis, or just obtaning the Par Swaps Fixed rates.

Every Libor can be obtaint in the same way.

• Thanks for the answer! So basically, you just look at the swaps that pay 6M LIBOR in the market and you make a graph of the swap rate for each swap maturity? I do not follow your second point entirely. What do you mean with 3M-6M Libor basis? Can you perhaps share some relevant documentation? Feb 15 '18 at 15:40
• Well, now a days the most liquid and used Libor curve would be the OIS. A few years ago is was the L3M Swap Curve, and every other Libor had a basis towards the 3M. Pretty much a credit risk between a 3M floating leg vs 6m floating leg. In that way you can now your exposure in those 3M between each reset. You can also obtaint Par Swap Rates for 6M Libor Swap from brokers. Feb 15 '18 at 15:43
• That doesn't really answer the question of what is represented by, say, ON, 1W, 2W, etc maturities on the, say, 6M LIBOR curve. I would have thought that the first maturity should be equal to the tenor of the index, e.g. 6M maturity for 6M LIBOR, since this is the period over which the interest is earned. So it't not clear what those lower maturities represent. Thank you Oct 16 '20 at 12:20