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An Efficient IMEX Compact Scheme for the Coupled Time Fractional Integro-Differential Equations Arising from Option Pricing with Jumps

Author

Listed:
  • Yong Chen

    (Xihua University)

  • Liangliang Li

    (Xihua University)

Abstract

When solving time fractional partial integro-differential equations (PIDEs) using standard finite difference methods, we have to invert the dense matrices arising from the discretization of the integral terms and this causes significant computational cost. In this paper, we develop an implicit-explicit (IMEX) compact finite difference scheme to raise computational efficiency when solving the coupled time fractional PIDEs arising in option pricing with jumps. First, we propose a new IMEX scheme for temporal discretization and compact finite difference scheme for spatial discretization. Then such high-order numerical scheme is proved to be unconditionally stable in the sense of the discrete $$L^2$$ L 2 and $$L^\infty$$ L ∞ norms. Finally, ample numerical experiments are reported to test the convergence rates of the proposed numerical scheme, and show its feasibility and applicability for the option pricing problems.

Suggested Citation

  • Yong Chen & Liangliang Li, 2025. "An Efficient IMEX Compact Scheme for the Coupled Time Fractional Integro-Differential Equations Arising from Option Pricing with Jumps," Computational Economics, Springer;Society for Computational Economics, vol. 65(4), pages 2397-2422, April.
    • Handle: RePEc:kap:compec:v:65:y:2025:i:4:d:10.1007_s10614-024-10642-0
    DOI: 10.1007/s10614-024-10642-0
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    References listed on IDEAS

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    1. Meihui Zhang & Xiangcheng Zheng, 2023. "Numerical Approximation to a Variable-Order Time-Fractional Black–Scholes Model with Applications in Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 1155-1175, October.
    2. Bertram During & Alexander Pitkin, 2017. "High-order compact finite difference scheme for option pricing in stochastic volatility jump models," Papers 1704.05308, arXiv.org, revised Feb 2019.
    3. Ionut Florescu & Ruihua Liu & Maria Cristina Mariani & Granville Sewell, 2013. "Numerical Schemes For Option Pricing In Regime-Switching Jump Diffusion Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1-25.
    4. Jumarie, Guy, 2008. "Stock exchange fractional dynamics defined as fractional exponential growth driven by (usual) Gaussian white noise. Application to fractional Black-Scholes equations," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 271-287, February.
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