On Multistep Stabilizing Correction Splitting Methods with Applications to the Heston Model

TL;DR

This paper introduces multistep stabilizing correction splitting methods that improve stability and are effective for the Heston model in financial mathematics, offering an alternative to traditional one-step methods.

Contribution

It develops new multistep stabilizing correction methods using high-order extrapolation, with proven stability and convergence, and demonstrates their effectiveness on the Heston model.

Findings

Methods are stable and convergent.

Competitive with existing splitting methods.

Effective in financial modeling applications.

Abstract

In this note we consider splitting methods based on linear multistep methods and stabilizing corrections. To enhance the stability of the methods, we employ an idea of Bruno & Cubillos (2016) who combine a high-order extrapolation formula for the explicit term with a formula of one order lower for the implicit terms. Several examples of the obtained multistep stabilizing correction methods are presented, and results on linear stability and convergence are derived. The methods are tested in the application to the well-known Heston model arising in financial mathematics and are found to be competitive with well-established one-step splitting methods from the literature.