A Fourier Interpolation Method for Numerical Solution of FBSDEs: Global Convergence, Stability, and Higher Order Discretizations

The convolution method for the numerical solution of forward-backward stochastic differential equations (FBSDEs) was originally formulated using Euler time discretizations and a uniform space grid. In this paper, we utilize tree-like spatial discretization that approximates BSDE on tree, so no interpolation procedure is necessary. addition to suppressing extrapolation error, leading globally convergent FBSDE, provide explicit convergence rates. On alternative grid conditional expectations involved in are computed Fourier analysis fast transform (FFT) algorithm. then extended higher-order FBSDEs. Numerical results demonstrating presented commodity price model, incorporating seasonality, forward prices.