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<p>We introduce a normalized time-fractional Black–Scholes (TFBS) model. Under this formulation, we develop a finite difference scheme on a nonuniform grid for the normalized TFBS equation. The grid is obtained through a locally optimal point-removal process followed by a two-stage nonlinear fitting step. Fewer grid points are used overall, while accuracy near the strike price is retained. Numerical results indicate a clear reduction in computational effort and demonstrate the suitability of the proposed approach.</p>

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An efficient numerical scheme on nonuniform grids for a normalized time-fractional Black–Scholes equation

  • 期刊论文

  • 发表日期：

    2026年3月24日

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  • Zhengang Li,
  • Yunjae Nam,
  • Juho Ma,
  • Youngjin Hwang,
  • Junseok Kim

摘要

We introduce a normalized time-fractional Black–Scholes (TFBS) model. Under this formulation, we develop a finite difference scheme on a nonuniform grid for the normalized TFBS equation. The grid is obtained through a locally optimal point-removal process followed by a two-stage nonlinear fitting step. Fewer grid points are used overall, while accuracy near the strike price is retained. Numerical results indicate a clear reduction in computational effort and demonstrate the suitability of the proposed approach.