Double sweep LU decomposition for American options under negative rates

TL;DR

This paper proposes a double sweep LU decomposition method to accurately solve American option pricing problems under negative interest rates, addressing limitations of the classic Brennan-Schwartz algorithm.

Contribution

It introduces a double sweep approach that ensures exact solutions for American options with two exercise boundaries under negative rates, extending previous methods.

Findings

Double sweep LU decomposition recovers exact solutions.

Method handles two exercise boundaries effectively.

Improves accuracy under negative interest rates.

Abstract

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.