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

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 time step $h$ higher than $\mathcal{O}$$(√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 R⁴⁸. The paper is self-contained and the code will be made freely downloadable.