In the article about Exercise boundaries of American options by F.AitSahlia and T.L.Lai the closed-form formulas for lower and upper bounds of the exercise boundaries are given as follows:
It appears that lower bound is always above the upper bound, which seems to be wrong. Let's assume parameters:
rho = 0.5,
alpha= 0.1 and
s = -2.5. Hence,
theta = -0.95. It leads to ln[theta/(theta-1)] entering the second formula as a positive term. Therefore the lower bound is above the upper bound.
The question is whether the reasoning above has a flaw?
"Exercise boundaries and efficient approximations to American option prices and hedge parameters" by F.AitSahlia and T.L.Lai