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Improved numerical solution of multi-asset option pricing problem: A localized RBF-FD approach

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  • Soleymani, Fazlollah
  • Akgül, Ali

Abstract

The objective of this work is to present a novel procedure for tackling European multi-asset option problems, which are modeled mathematically in terms of time-dependent parabolic partial differential equations with variable coefficients. To use as low as possible of number computational grid points, a non-uniform grid is generated while a radial basis function-finite difference scheme with the Gaussian function is applied on such a grid to discretize the model as efficiently as possible. To reduce the burdensome for tackling the resulting set of ordinary differential equations, a Krylov method, which is due to the application of exponential matrix function on a vector, is taken into account. The combination of these techniques reduces the computational effort and the elapsed time. Several experiments are brought froward to illustrate the superiority of the new improved approach. In fact, the contributed procedure is capable to tackle even 6D PDEs on a normally-equipped computer quickly and efficiently.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:119:y:2019:i:c:p:298-309
    DOI: 10.1016/j.chaos.2019.01.003
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    References listed on IDEAS

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    1. Arismendi, Juan & Genaro, Alan De, 2016. "A Monte Carlo multi-asset option pricing approximation for general stochastic processes," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 75-99.
    2. Tristan Guillaume, 2016. "An Analytically Tractable Model for Pricing Multiasset Options with Correlated Jump-Diffusion Equity Processes and a Two-Factor Stochastic Yield Curve," Journal of Applied Mathematics, Hindawi, vol. 2016, pages 1-14, October.
    3. Lord, G.J. & Stone, D., 2017. "New efficient substepping methods for exponential timestepping," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 342-365.
    4. Karipova, Gulnur & Magdziarz, Marcin, 2017. "Pricing of basket options in subdiffusive fractional Black–Scholes model," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 245-253.
    5. Li, Huanhuan & Chen, Diyi & Zhang, Hao & Wu, Changzhi & Wang, Xiangyu, 2017. "Hamiltonian analysis of a hydro-energy generation system in the transient of sudden load increasing," Applied Energy, Elsevier, vol. 185(P1), pages 244-253.
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    Cited by:

    1. Yang, Xiangfeng & Zhang, Zhiqiang & Gao, Xin, 2019. "Asian-barrier option pricing formulas of uncertain financial market," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 79-86.
    2. 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).
    3. Gao, Rong & Wu, Wei & Lang, Chao & Lang, Liying, 2020. "Geometric Asian barrier option pricing formulas of uncertain stock model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

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