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<p>In this paper, we employ classical implicit-explicit Runge-Kutta (IMEX RK) methods to solve European option pricing problems for jump-diffusion models with nonsmooth payoff functions, which depict financial markets more realistically than the classic Black-Scholes model. We prove the stability and convergence of the proposed methods under the conditions that the associated differentiation matrix is positive definite and the time step-size meets specific constraints. This matrix is constructed from convolution summation coefficients of the differential form, derived via novel discrete orthogonal convolution kernels. We rigorously analyze the consistency error of the scheme near singularities induced by nonsmooth payoff functions, and conduct numerical experiments to verify the stability and convergence of IMEX RK methods with up to fourth-order accuracy. In addition, we adopt graded time grids and adaptive time-stepping strategies to mitigate numerical errors near such singularities.</p>

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A variable step-size implicit-explicit runge-kutta approach to option pricing for jump-diffusion models with nonsmooth payoff functions

  • 期刊论文

  • 发表日期：

    2026年6月16日

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  • Jincheng Ren,
  • Shiyu He

摘要

In this paper, we employ classical implicit-explicit Runge-Kutta (IMEX RK) methods to solve European option pricing problems for jump-diffusion models with nonsmooth payoff functions, which depict financial markets more realistically than the classic Black-Scholes model. We prove the stability and convergence of the proposed methods under the conditions that the associated differentiation matrix is positive definite and the time step-size meets specific constraints. This matrix is constructed from convolution summation coefficients of the differential form, derived via novel discrete orthogonal convolution kernels. We rigorously analyze the consistency error of the scheme near singularities induced by nonsmooth payoff functions, and conduct numerical experiments to verify the stability and convergence of IMEX RK methods with up to fourth-order accuracy. In addition, we adopt graded time grids and adaptive time-stepping strategies to mitigate numerical errors near such singularities.