Pricing American options under negative rates

This paper starts by defining the criteria where the early-exercise of an American option is never optimal, under positive, or negative rates. It follows with a short analysis of the various shapes of the exercise region under negative interest rates. It then presents a new integral equation, which establishes the option price, and the two early exercise boundaries, under negative rates. It shows how to solve this new equation, through modifications of the modern and efficient algorithm of Andersen and Lake, from the initial guess of the two boundaries to more subtle changes required in their fixed point method for stability. Finally, the performance and accuracy of the resulting algorithm is assessed against a cutting edge finite difference method implementation.