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<p>In this work, we introduce a fourth-order numerical scheme for the generalized Black-Scholes equation (BSE) governing the option price. We approximate the time derivative using the Crank-Nicolson finite difference approach, and the quartic B-spline approach is employed for the spatial direction to construct the fully discrete scheme. The propose scheme is fourth order in the spatial direction and second order in the temporal direction. This scheme is unconditionally stable, as shown by the von Neumann stability analysis. In the end, we analyze some European option cases to demonstrate the accuracy and efficiency of the propose scheme. The outcomes of the experiment illustrate the superiority of the present method over existing numerical algorithms.</p>

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A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making

  • 期刊论文

  • 发表日期：

    2025年7月19日

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  • Ramesh Ojha,
  • Srinivasan Natesan

摘要

In this work, we introduce a fourth-order numerical scheme for the generalized Black-Scholes equation (BSE) governing the option price. We approximate the time derivative using the Crank-Nicolson finite difference approach, and the quartic B-spline approach is employed for the spatial direction to construct the fully discrete scheme. The propose scheme is fourth order in the spatial direction and second order in the temporal direction. This scheme is unconditionally stable, as shown by the von Neumann stability analysis. In the end, we analyze some European option cases to demonstrate the accuracy and efficiency of the propose scheme. The outcomes of the experiment illustrate the superiority of the present method over existing numerical algorithms.