Boundary error control for numerical solution of BSDEs by the convolution-FFT method

Fuente: arXiv
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Main Authors: Gao, Xiang, Hyndman, Cody
Format: Preprint
Published: 2025
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author Gao, Xiang
Hyndman, Cody
author_facet Gao, Xiang
Hyndman, Cody
contents We first review the convolution fast-Fourier-transform (CFFT) approach for the numerical solution of backward stochastic differential equations (BSDEs) introduced in (Hyndman and Oyono Ngou, 2017). We then propose a method for improving the boundary errors obtained when valuing options using this approach. We modify the damping and shifting schemes used in the original formulation, which transforms the target function into a bounded periodic function so that Fourier transforms can be applied successfully. Time-dependent shifting reduces boundary error significantly. We present numerical results for our implementation and provide a detailed error analysis showing the improved accuracy and convergence of the modified convolution method.
format Preprint
id arxiv_https___arxiv_org_abs_2512_24714
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Boundary error control for numerical solution of BSDEs by the convolution-FFT method
Gao, Xiang
Hyndman, Cody
Numerical Analysis
Probability
Computational Finance
65T50, 60H35 (Primary) 91G60, 60H30 (Secondary)
We first review the convolution fast-Fourier-transform (CFFT) approach for the numerical solution of backward stochastic differential equations (BSDEs) introduced in (Hyndman and Oyono Ngou, 2017). We then propose a method for improving the boundary errors obtained when valuing options using this approach. We modify the damping and shifting schemes used in the original formulation, which transforms the target function into a bounded periodic function so that Fourier transforms can be applied successfully. Time-dependent shifting reduces boundary error significantly. We present numerical results for our implementation and provide a detailed error analysis showing the improved accuracy and convergence of the modified convolution method.
title Boundary error control for numerical solution of BSDEs by the convolution-FFT method
topic Numerical Analysis
Probability
Computational Finance
65T50, 60H35 (Primary) 91G60, 60H30 (Secondary)
url https://arxiv.org/abs/2512.24714