A high-order recombination algorithm for weak approximation of stochastic differential equations

Abstract

This paper presents an algorithm for applying the high-order recombination method, originally introduced by Lyons and Litterer in ``High-order recombination and an application to cubature on Wiener space'' (Ann. Appl. Probab. 22(4):1301--1327, 2012), to practical problems in mathematical finance. A refined error analysis is provided, yielding a sharper condition for space partitioning. Based on this condition, a computationally feasible recursive partitioning algorithm is developed. Numerical examples are also included, demonstrating that the proposed algorithm effectively avoids the explosive growth in the cardinality of the support required to achieve high-order approximations.