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?