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

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  • Polynice Oyono Ngou

    (Department of Mathematics and Statistics, Concordia University, 1455 Boulevard de Maisonneuve Ouest, Montréal, QC H3G 1M8, Canada)

  • Cody Hyndman

    (Department of Mathematics and Statistics, Concordia University, 1455 Boulevard de Maisonneuve Ouest, Montréal, QC H3G 1M8, Canada)

Abstract

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

Suggested Citation

  • Polynice Oyono Ngou & Cody Hyndman, 2022. "A Fourier Interpolation Method for Numerical Solution of FBSDEs: Global Convergence, Stability, and Higher Order Discretizations," JRFM, MDPI, vol. 15(9), pages 1-32, August.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:9:p:388-:d:903002
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