August 21st, 2017, 1:23 pm
Hi - SABR (forward interest rate) model, cannot model the joint evolution of forward rates, as it should take their correlation into account as well as evolving them under a single measure. To take those two requirements into account you need to resort to SABR-Libor Market Model.
The industry uses SABR to price swaptions, however not through a SABR (forward interest rate) model but through a SABR (forward swap) model, where you model directly the swap rate.
Hope this helps.