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 timestep h higher than O(root 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 R-48. The paper is self-contained and the code will be made freely downloadable.