An efficient third-order scheme for BSDEs based on nonequidistant difference scheme

In this paper, we propose an efficient third-order numerical scheme for backward stochastic differential equations(BSDEs). We use 3-point Gauss-Hermite quadrature rule for approximation of the conditional expectation and avoid spatial interpolation by setting up a fully nested spatial grid and using the approximation of derivatives based on nonequidistant sample points. As a result, the overall computational complexity is reduced significantly. Several examples show that the proposed scheme is of third order and very efficient.