Convergence of the Approximation scheme to American option pricing via the discrete Morse semiflow

TL;DR

This paper analyzes the convergence rate of a discrete Morse semiflow approximation scheme for American call options, demonstrating both solution and free boundary convergence.

Contribution

It introduces a new convergence rate analysis for the approximation scheme of American options using the discrete Morse semiflow.

Findings

Established a convergence rate for the approximate solutions.

Proved convergence of the approximate free boundaries.

Validated the effectiveness of the scheme for American option pricing.

Abstract

We consider the approximation scheme of the American call option via the discrete Morse semiflow. It is the minimizing scheme of a time-semidiscretized variational functional. In this paper we obtain a rate of convergence of approximate solutions. In addition, the convergence of approximate free boundaries is proved.