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<p>In this work, we introduce an efficient compact finite difference (CFD) method for solving the time-fractional Black-Scholes (TFBS) option pricing model. The time-fractional derivative is described using Caputo-Fabrizio (C-F) fractional derivative, and a compact finite difference method is employed to discretize the spatial derivative. The main contribution of this work is to develop a high-order discrete scheme for the TFBS model. In the numerical scheme, we have developed a convergence rate of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13660_2025_3261_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="MATHML"><math> <mi>O</mi> <mo stretchy="false">(</mo> <msup> <mi>τ</mi> <mn>2</mn> </msup> <mo>+</mo> <msup> <mi>h</mi> <mn>4</mn> </msup> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$O(\tau ^{2} + h^{4})$</EquationSource> </InlineEquation>, where <i>τ</i> denotes the temporal step and <i>h</i> represents the spatial step. To verify the effectiveness of the proposed method, we have conducted stability analysis and error estimation using the Fourier method. Furthermore, a series of numerical experiments were conducted, and the numerical results demonstrated the theoretical order of accuracy and illustrated the effectiveness of the proposed method.</p>

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A compact finite difference scheme for solving fractional Black-Scholes option pricing model

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  • 出版模式：

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  • 发表日期：

    2025年3月18日

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  • Yuelong Feng,
  • Xindong Zhang,
  • Yan Chen,
  • Leilei Wei

摘要

In this work, we introduce an efficient compact finite difference (CFD) method for solving the time-fractional Black-Scholes (TFBS) option pricing model. The time-fractional derivative is described using Caputo-Fabrizio (C-F) fractional derivative, and a compact finite difference method is employed to discretize the spatial derivative. The main contribution of this work is to develop a high-order discrete scheme for the TFBS model. In the numerical scheme, we have developed a convergence rate of O ( τ 2 + h 4 ) $O(\tau ^{2} + h^{4})$ , where τ denotes the temporal step and h represents the spatial step. To verify the effectiveness of the proposed method, we have conducted stability analysis and error estimation using the Fourier method. Furthermore, a series of numerical experiments were conducted, and the numerical results demonstrated the theoretical order of accuracy and illustrated the effectiveness of the proposed method.