A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations
For researchers in computational finance and stochastic processes, this provides a practical comparison of higher-order schemes for stopped diffusions, though it is an incremental implementation and comparison study.
The paper reviews, implements, and compares higher-order weak numerical schemes for stopped stochastic differential equations, achieving convergence rates better than O(√h). The schemes are tested on problems up to ℝ⁴⁸, with accuracy and computational cost compared.
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.