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<p>This paper proposes a high-order numerical method for pricing arithmetic Asian options under the Black–Scholes PDE framework. The key innovation is the use of a modified fourth-order finite difference scheme to discretize the diffusion term, enhancing spatial accuracy by incorporating both function values and adjacent first derivatives. This formulation is embedded within a cubic B-spline collocation framework, while Crank–Nicolson time integration ensures second-order temporal accuracy. Numerical results confirm the scheme’s stability, consistency, and fourth-order spatial convergence, with a total computational complexity of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10614_2025_11156_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="53" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathcal {O}(M^2)\)</EquationSource> </InlineEquation> when the number of time steps scales linearly with the <i>M</i> number of spatial grid points.</p>

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A Computationally Efficient Hybrid Numerical Method for Asian Option Pricing in the Black-Scholes Framework

  • 期刊论文

  • 发表日期：

    2025年11月13日

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  • Liju P,
  • Ashish Awasthi

摘要

This paper proposes a high-order numerical method for pricing arithmetic Asian options under the Black–Scholes PDE framework. The key innovation is the use of a modified fourth-order finite difference scheme to discretize the diffusion term, enhancing spatial accuracy by incorporating both function values and adjacent first derivatives. This formulation is embedded within a cubic B-spline collocation framework, while Crank–Nicolson time integration ensures second-order temporal accuracy. Numerical results confirm the scheme’s stability, consistency, and fourth-order spatial convergence, with a total computational complexity of \(\mathcal {O}(M^2)\) when the number of time steps scales linearly with the M number of spatial grid points.