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The Use of Partial Fractional Form of A-Stable Padé Schemes for the Solution of Fractional Diffusion Equation with Application in Option Pricing

Author

Listed:
  • H. Ghafouri

    (Azarbaijan Shahid Madani University)

  • M. Ranjbar

    (Azarbaijan Shahid Madani University)

  • A. Khani

    (Azarbaijan Shahid Madani University)

Abstract

In this work, we propose a numerical technique based on the Padé scheme for solving the two-sided space-fractional diffusion equation. First, space fractional diffusion equations are approximated with respect to space variable. We will achieve a system of ODE. Then by applying a parallel implementation of the A-stable methods, this system is solved. Also, we use of the presented method for pricing European call option under a geometric Lévy process. Illustrative examples are included to show the accuracy and applicability of the new technique presented in the current paper.

Suggested Citation

  • H. Ghafouri & M. Ranjbar & A. Khani, 2020. "The Use of Partial Fractional Form of A-Stable Padé Schemes for the Solution of Fractional Diffusion Equation with Application in Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 56(4), pages 695-709, December.
    • Handle: RePEc:kap:compec:v:56:y:2020:i:4:d:10.1007_s10614-019-09927-6
    DOI: 10.1007/s10614-019-09927-6
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    References listed on IDEAS

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    1. Dehestani, H. & Ordokhani, Y. & Razzaghi, M., 2018. "Fractional-order Legendre–Laguerre functions and their applications in fractional partial differential equations," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 433-453.
    2. Peter Carr & Liuren Wu, 2003. "The Finite Moment Log Stable Process and Option Pricing," Journal of Finance, American Finance Association, vol. 58(2), pages 753-777, April.
    3. Liu, Q. & Liu, F. & Gu, Y.T. & Zhuang, P. & Chen, J. & Turner, I., 2015. "A meshless method based on Point Interpolation Method (PIM) for the space fractional diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 930-938.
    4. Cartea, Álvaro & del-Castillo-Negrete, Diego, 2007. "Fractional diffusion models of option prices in markets with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 749-763.
    5. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    6. repec:bla:jfinan:v:58:y:2003:i:2:p:753-778 is not listed on IDEAS
    7. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
    8. Khaliq, A.Q.M. & Voss, D.A. & Yousuf, M., 2007. "Pricing exotic options with L-stable Pade schemes," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3438-3461, November.
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    Cited by:

    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.

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