Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality )
Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I would say it is when the swaption worths less than the underlying swap. When such condition arises ?
Can we assume that if it is not optimal to exercise the payer swaption then the receiver swaption exercise is optimal. (Intuitively if such preposition is true than the call put parity exists)
An other question, let say I have a callable payer swap by both counterpaties. Hence I am long a payer swap + receiver bermuda and short a payer bermuda to my cpty. Is the fact that if one cpty exercises the call, the option of the other will definitly expire worthless, allows me to say that there is call-put parity in this case and I am in a position of a payer swap and forward receiver ? In a nutshul I have all in all a short maturity swap with maturity equals the first exercise date ? Or there is still a world state where it is not optimal to exercise for both cpties ?