Schwarz Modulus Based Matrix Splittings with Minimal Polynomial Extrapolation Acceleration for linear complementarity problems arising from American option pricing

TL;DR

This paper presents a new Schwarz modulus-based splitting method combined with Modified Polynomial Extrapolation to efficiently solve linear complementarity problems in American option pricing, significantly reducing iteration counts.

Contribution

The authors introduce a novel splitting method and acceleration technique specifically designed for linear complementarity problems in American option pricing, improving computational efficiency.

Findings

Near tenfold reduction in iteration counts compared to classical methods.

Effective acceleration of convergence using Polynomial Extrapolation.

Applicable to problems arising from American option pricing models.

Abstract

Pricing American options is more complicated than pricing European options, because they can be exercised at any time, and one thus needs to solve a linear complementarity problem instead of simply doing time stepping for computing European options. We introduce a new Schwarz modulus-based splitting method for solving such linear complementarity problems, and further accelerate them using Modified Polynomial Extrapolation, a non-linear vector sequence acceleration technique, which is very much related to Krylov methods in the linear case. Numerical experiments on a model problem show that our new solver can have close to an order of magnitude lower iteration counts than the classically used modulus-based matrix splitting technique.