A Novel Second Order Scheme with One Step for Forward Backward Stochastic Differential Equations

Abstract

In this paper, we design a novel explicit second order scheme with one step for forward backward stochastic differential equations, and the Crank-Nicolson scheme is a specific case of our proposed framework. We first establish a rigorous stability result, and then we derive precise error estimates. Moreover, we confirm that the proposed novel scheme is second order convergent. The theoretical results for the proposed methods are supported by numerical experiments.