I am confused on the following:
When we price swaption, the market convention is to use Black's Model which assumes forward swap rate is following Black's model under the Q(t) measure.
When we tries to use SABR, the forward swap rate is again model depending on the value of Beta.
If we were to calibrate SABR for Swaption volatility, will there be a inconsistency with specifying the model for forward swap rate?
Thanks for clarifying