IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v185y2024ics0960077924007082.html
   My bibliography  Save this article

Solving multi-dimensional European option pricing problems by integrals of the inverse quadratic radial basis function on non-uniform meshes

Author

Listed:
  • Liu, Tao
  • Soleymani, Fazlollah
  • Ullah, Malik Zaka

Abstract

This paper explores multi-asset options as a means to diversify portfolios, mitigating risk across various assets. We present a numerical method using radial basis function-generated finite difference solvers via integrals of the inverse quadratic kernel. Our method introduces new weights for the task we are dealing with. We derive and compute analytical solutions to approximate function derivatives on three-node stencils with non-uniform and uniform distances. Our findings highlight the convergence order of the proposed analytical weights. Numerical examples illustrate the theory.

Suggested Citation

  • Liu, Tao & Soleymani, Fazlollah & Ullah, Malik Zaka, 2024. "Solving multi-dimensional European option pricing problems by integrals of the inverse quadratic radial basis function on non-uniform meshes," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    • Handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007082
    DOI: 10.1016/j.chaos.2024.115156
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924007082
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115156?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Cavoretto, Roberto, 2022. "Adaptive LOOCV-based kernel methods for solving time-dependent BVPs," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    2. Chen, Chuin-Shan & Noorizadegan, Amir & Young, D.L. & Chen, C.S., 2023. "On the selection of a better radial basis function and its shape parameter in interpolation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    3. Shi, Lei & Ullah, Malik Zaka & Nashine, Hemant Kumar, 2024. "On the construction of a quartically convergent method for high-dimensional Black-Scholes time-dependent PDE," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    4. Milovanović, Slobodan & von Sydow, Lina, 2020. "A high order method for pricing of financial derivatives using Radial Basis Function generated Finite Differences," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 205-217.
    5. Lishang Jiang, 2005. "Mathematical Modeling and Methods of Option Pricing," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 5855, February.
    6. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.
    7. Soleymani, Fazlollah & Akgül, Ali, 2019. "Improved numerical solution of multi-asset option pricing problem: A localized RBF-FD approach," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 298-309.
    8. Wang, Jian & Wen, Shuai & Yang, Mengdie & Shao, Wei, 2022. "Practical finite difference method for solving multi-dimensional black-Scholes model in fractal market," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Shi, Lei & Ullah, Malik Zaka & Nashine, Hemant Kumar, 2024. "On the construction of a quartically convergent method for high-dimensional Black-Scholes time-dependent PDE," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    2. Li, Yang & Liu, Dejun & Yin, Zhexu & Chen, Yun & Meng, Jin, 2023. "Adaptive selection strategy of shape parameters for LRBF for solving partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 440(C).
    3. Noorizadegan, A. & Young, D.L. & Hon, Y.C. & Chen, C.S., 2024. "Power-enhanced residual network for function approximation and physics-informed inverse problems," Applied Mathematics and Computation, Elsevier, vol. 480(C).
    4. Hong-Ming Yin & Jin Liang & Yuan Wu, 2018. "On a New Corporate Bond Pricing Model with Potential Credit Rating Change and Stochastic Interest Rate," JRFM, MDPI, vol. 11(4), pages 1-12, December.
    5. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Shoaib, Muhammad & Kiani, Adiqa Kausar, 2022. "Fractional order Lorenz based physics informed SARFIMA-NARX model to monitor and mitigate megacities air pollution," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    6. Hyong-chol O & Song-San Jo, 2019. "Variational inequality for perpetual American option price and convergence to the solution of the difference equation," Papers 1903.05189, arXiv.org.
    7. Zheng, Sanpeng & Feng, Renzhong, 2023. "A variable projection method for the general radial basis function neural network," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    8. Hyong-Chol O & Mun-Chol KiM, 2013. "The Pricing of Multiple-Expiry Exotics," Papers 1302.3319, arXiv.org, revised Aug 2013.
    9. Ben Boukai, 2021. "On the RND under Heston's stochastic volatility model," Papers 2101.03626, arXiv.org.
    10. Tao Liu & Malik Zaka Ullah & Stanford Shateyi & Chao Liu & Yanxiong Yang, 2023. "An Efficient Localized RBF-FD Method to Simulate the Heston–Hull–White PDE in Finance," Mathematics, MDPI, vol. 11(4), pages 1-15, February.
    11. Ben Boukai, 2021. "The Generalized Gamma distribution as a useful RND under Heston's stochastic volatility model," Papers 2108.07937, arXiv.org, revised Aug 2021.
    12. Karim, Md Aktar Ul & Aithal, Vikram & Bhowmick, Amiya Ranjan, 2023. "Random variation in model parameters: A comprehensive review of stochastic logistic growth equation," Ecological Modelling, Elsevier, vol. 484(C).
    13. Ardian, Aldin & Kumral, Mustafa, 2020. "Incorporating stochastic correlations into mining project evaluation using the Jacobi process," Resources Policy, Elsevier, vol. 65(C).
    14. Yaroslav D. Sergeyev & Maria Chiara Nasso & Daniela Lera, 2024. "Numerical methods using two different approximations of space-filling curves for black-box global optimization," Journal of Global Optimization, Springer, vol. 88(3), pages 707-722, March.
    15. Petr Fedoseev & Artur Karimov & Vincent Legat & Denis Butusov, 2022. "Preference and Stability Regions for Semi-Implicit Composition Schemes," Mathematics, MDPI, vol. 10(22), pages 1-13, November.
    16. Deepak Kumar Yadav & Akanksha Bhardwaj & Alpesh Kumar, 2024. "Operator Splitting Method to Solve the Linear Complementarity Problem for Pricing American Option: An Approximation of Error," Computational Economics, Springer;Society for Computational Economics, vol. 64(6), pages 3353-3379, December.
    17. Hanyue Huang & Qiguo Sun & Xibei Yang, 2025. "Stochastic Optimal Control of Iron Condor Portfolios for Profitability and Risk Management," Papers 2501.12397, arXiv.org.
    18. Marchetti, F., 2024. "A fast surrogate cross validation algorithm for meshfree RBF collocation approaches," Applied Mathematics and Computation, Elsevier, vol. 481(C).
    19. Hosseinzadeh, Hossein & Sedaghatjoo, Zeinab, 2025. "Radial boundary elements method, a new approach on using radial basis functions to solve partial differential equations, efficiently," Applied Mathematics and Computation, Elsevier, vol. 493(C).
    20. Hyong-chol O & Yong-hwa Ro & Ning Wan, 2014. "A Method of Reducing Dimension of Space Variables in Multi-dimensional Black-Scholes Equations," Papers 1406.2053, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:185:y:2024:i:c:s0960077924007082. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.