A Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme for American Options

TL;DR

This paper introduces a new a posteriori error estimator for American option pricing using a front-fixing finite difference scheme, enabling adaptive grid refinement to meet specified accuracy levels.

Contribution

It develops a Richardson-based error estimator specifically for American options, facilitating adaptive mesh selection for improved numerical accuracy.

Findings

The estimator accurately predicts errors in option price and free boundary.

Adaptive grid refinement achieves desired error tolerances efficiently.

The MATLAB implementation demonstrates practical applicability.

Abstract

For the numerical solution of the American option valuation problem, we provide a script written in MATLAB implementing an explicit finite difference scheme. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson's extrapolation theory. This error estimator allows us to find a suitable grid where the computed solution, both the option price field variable and the free boundary position, verify a prefixed error tolerance.