Error estimates for finite difference approximations of American put option price

TL;DR

This paper provides error estimates for finite difference methods applied to multi-asset American put options, considering variable asset dynamics and domain restrictions, with proven convergence rates.

Contribution

It introduces rigorous error bounds for finite difference approximations of multi-asset American options, including domain truncation effects, under variable drift and volatility.

Findings

Error of order 0.25 in time discretization

Error of order 0.5 in space discretization

Error estimates for domain restriction effects

Abstract

Finite difference approximations to multi-asset American put option price are considered. The assets are modelled as a multi-dimensional diffusion process with variable drift and volatility. Approximation error of order one quarter with respect to the time discretisation parameter and one half with respect to the space discretisation parameter is proved by reformulating the corresponding optimal stopping problem as a solution of a degenerate Hamilton-Jacobi-Bellman equation. Furthermore, the error arising from restricting the discrete problem to a finite grid by reducing the original problem to a bounded domain is estimated.