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A high order method for pricing of financial derivatives using Radial Basis Function generated Finite Differences

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  • Milovanović, Slobodan
  • von Sydow, Lina

Abstract

In this paper, we consider the numerical pricing of financial derivatives using Radial Basis Function generated Finite Differences in space. Such discretization methods have the advantage of not requiring Cartesian grids. Instead, the nodes can be placed with higher density in areas where there is a need for higher accuracy. Still, the discretization matrix is fairly sparse. As a model problem, we consider the pricing of European options in 2D. Since such options have a discontinuity in the first derivative of the payoff function which prohibits high order convergence, we smooth this function using an established technique for Cartesian grids. Numerical experiments show that we acquire a fourth order scheme in space, both for the uniform and the nonuniform node layouts that we use. The high order method with the nonuniform node layout achieves very high accuracy with relatively few nodes. This renders the potential for solving pricing problems in higher spatial dimensions since the computational memory and time demand become much smaller with this method compared to standard techniques.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:174:y:2020:i:c:p:205-217
    DOI: 10.1016/j.matcom.2020.02.005
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    References listed on IDEAS

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    1. Slobodan Milovanovi'c & Lina von Sydow, 2018. "A High Order Method for Pricing of Financial Derivatives using Radial Basis Function generated Finite Differences," Papers 1808.05890, arXiv.org, revised Aug 2018.
    2. Slobodan Milovanovi'c, 2018. "Pricing Financial Derivatives using Radial Basis Function generated Finite Differences with Polyharmonic Splines on Smoothly Varying Node Layouts," Papers 1808.02365, arXiv.org, revised Aug 2018.
    3. Persson, Jonas & von Sydow, Lina, 2010. "Pricing American options using a space-time adaptive finite difference method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1922-1935.
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    Citations

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    Cited by:

    1. Lyu, Jisang & Park, Eunchae & Kim, Sangkwon & Lee, Wonjin & Lee, Chaeyoung & Yoon, Sungha & Park, Jintae & Kim, Junseok, 2021. "Optimal non-uniform finite difference grids for the Black–Scholes equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 690-704.
    2. Černá, Dana & Fiňková, Kateřina, 2024. "Option pricing under multifactor Black–Scholes model using orthogonal spline wavelets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 309-340.
    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. Cho, Junhyun & Kim, Yejin & Lee, Sungchul, 2022. "An accurate and stable numerical method for option hedge parameters," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    5. Gholamreza Farahmand & Taher Lotfi & Malik Zaka Ullah & Stanford Shateyi, 2023. "Finding an Efficient Computational Solution for the Bates Partial Integro-Differential Equation Utilizing the RBF-FD Scheme," Mathematics, MDPI, vol. 11(5), pages 1-13, February.
    6. 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.

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