On a numerical approximation scheme for construction of the early exercise boundary for a class of nonlinear Black-Scholes equations

TL;DR

This paper develops a numerical scheme to approximate the early exercise boundary for nonlinear Black-Scholes equations with nonlinear volatility, transforming the problem into a nonlinear parabolic PDE and providing computational results.

Contribution

It introduces a method to construct the early exercise boundary for nonlinear Black-Scholes models by transforming it into a fixed-domain nonlinear PDE, with numerical implementation.

Findings

Numerical computation of the early exercise boundary for various nonlinear models.

The transformation simplifies the problem into a fixed domain nonlinear PDE.

Results demonstrate the effectiveness of the proposed numerical scheme.

Abstract

The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method how to transform the problem into a solution of a time depending nonlinear parabolic equation defined on a fixed domain. Results of numerical computation of the early exercise boundary for various nonlinear Black--Scholes equations are also presented.