  The classic Brennan-Schwartz algorithm to solve the linear complementary
problem, which arises from the finite difference discretization of the partial
differential equation related to American option pricing does not lead to the
exact solution under negative interest rates. This is due to the two exercise
boundaries which may appear under negative interest rate, while the algorithm
was proven to lead to the exact solution in the case of a single exercise
boundary only. This paper explains that two sweeps of the Brennan-Schwartz
algorithm in two directions is enough to recover the exact solution.

Computational Finance;Pricing of Securities