I'm new to the quant finance and have a very basic question about LIBOR curve.LIBOR is published every day for 4 different tenors (1M, 3M, 6M, 1Y), and each rate means how much annual interest should be paid when leading banks borrow money from another.In my understanding, there should be a unique LIBOR yield curve, in which 1M, 3M, 6M, 1Y point values are the same as the quoted value above.But it doesn't seem to be the case. There's a LIBOR curve for each 4 different tenors. Given this, what does the value of 1M LIBOR curve at 1Y point?And, when you model LIBOR using short rate model, you're modelling the unique LIBOR short rate, not the LIBOR of each tenor separately. Correct?Thx!

forgive me if this seems to be insensitive but I think you are confused. a LIBOR curve is usually constructed from deposit rates, futures and swaps and not from the levels of 1M, 2M, 3M, 6M etc LIBOR rates.

So you're saying that there's a "unique" LIBOR curve, which is built off from the LIBOR rates of various tenors?If that's the case, why do people say "3M discounting" or "1M discounting" instead of "the" LIBOR discounting?

Sadly, there is not a unique Libor curve any more (there effectively was one pre-crisis, or at least it was a commonly held belief), since there is a sense that longer tenor rates embed more credit risk than shorter ones. Empirically, you can observe that the 12M Libor rate is "too high" relative to a curve built from 3M cash + interpolated FRA or ED futures, and similar relationships hold for the other tenors. Discounting at OIS or more complicated CSA based curves, as is increasingly done in the swaps market, just adds to the complications. What this means in practice is that Libor curves constructed in this manner have no particular meaning outside of a very narrow use case valuing and risk managing derivatives. And it brings up nagging questions like "what does the 1M rate on the 3M Libor curve mean, and how do you construct it in a coherent manner?"

The 1Y point implied by the 1M LIBOR curve tells you the par rate on a swap where the floating side index is 1M LIBOR.

QuoteOriginally posted by: MartinghoulThe 1Y point implied by the 1M LIBOR curve tells you the par rate on a swap where the floating side index is 1M LIBOR.Agreed, but what if you swap the M and Y?

The 1M point implied by the 1Y (12M) LIBOR curve should tell you the par rate on a 1M FRA consistent with the 12M rate. Obviously, usual caveats would apply, probably more than they would otherwise.IMHO...

QuoteOriginally posted by: briankimBut it doesn't seem to be the case. There's a LIBOR curve for each 4 different tenors. Given this, what does the value of 1M LIBOR curve at 1Y point?And, when you model LIBOR using short rate model, you're modelling the unique LIBOR short rate, not the LIBOR of each tenor separately. Correct?Yes, you're right on both counts.There's a libor curve for each tenor. Simply because 1M libor rolled over 3 times is not equal to 3M libor rolled over 1 times.The 1M tenor still has less credit/liquidity risk owing to earlier repayment, and the basis spreads on the market reflect this phenomenon.It's easier to treat these 2 tenors as distinct, but correlated.As for modelling with short rates, again you're right. We pick the dominant tenor, usually 3M for USD, and diffuse the short rates for the 3M.If we need to back out 6M, or any other tenors, we apply the Day1 deterministic spread on top of what we had modelled.