A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

TL;DR

This paper reviews, implements, and compares higher-order numerical schemes for simulating stopped diffusions, focusing on accuracy and efficiency in high-dimensional problems, with practical code available for researchers.

Contribution

It provides a comprehensive comparison of higher-order weak numerical schemes for stopped SDEs, including implementation details and performance analysis in high dimensions.

Findings

Higher-order schemes achieve better accuracy than standard methods.

The implemented schemes are computationally efficient in high-dimensional settings.

The Matlab code facilitates practical application and further research.

Abstract

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the timestep $h$ higher than ${\cal O}(\sqrt{h})$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to ${\mathbb R}^{48}$. The paper is self-contained and the code will be made freely downloadable.