ADI schemes for pricing American options under the Heston model

TL;DR

This paper introduces a simple adaptation of ADI schemes for efficiently and accurately pricing American options under the Heston model, with extensive stability, convergence analysis, and a key theoretical proof.

Contribution

It presents a novel adaptation of ADI schemes specifically designed for American option pricing under the Heston model, including stability, convergence, and theoretical validation.

Findings

The adapted ADI schemes are stable and convergent in practical applications.

The methods effectively handle the partial differential complementarity problem.

A significant theoretical result supporting the methods is proved.

Abstract

In this paper a simple, effective adaptation of Alternating Direction Implicit (ADI) time discretization schemes is proposed for the numerical pricing of American-style options under the Heston model via a partial differential complementarity problem. The stability and convergence of the new methods are extensively investigated in actual, challenging applications. In addition a relevant theoretical result is proved.