I've been trying to calibrate Hull-white one factor model with swaption but I have a trouble making closed form solution of swaption
Below is the part of paper I've been referencing to
The problem is r* part.
In order to calculate the price of swaption following the instruction of the paper, I need to solve the equation (16) to come up with r*.
But it seems that there is no closed-form solution to this equation finding r*.
However, if no closed-form solution exists for pricing swaption, the whole calibration process takes too long. I think it is not what the author intended.
Is there any closed-form solution for finding r* in this equation?
Many thanks in advance for helping me.