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Solution of the Fractional Black‐Scholes Option Pricing Model by Finite Difference Method

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  • Lina Song
  • Weiguo Wang

Abstract

This work deals with the put option pricing problems based on the time‐fractional Black‐Scholes equation, where the fractional derivative is a so‐called modified Riemann‐Liouville fractional derivative. With the aid of symbolic calculation software, European and American put option pricing models that combine the time‐fractional Black‐Scholes equation with the conditions satisfied by the standard put options are numerically solved using the implicit scheme of the finite difference method.

Suggested Citation

  • Lina Song & Weiguo Wang, 2013. "Solution of the Fractional Black‐Scholes Option Pricing Model by Finite Difference Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:194286
    DOI: 10.1155/2013/194286
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    References listed on IDEAS

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    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
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    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    5. Halil Mete Soner & Guy Barles, 1998. "Option pricing with transaction costs and a nonlinear Black-Scholes equation," Finance and Stochastics, Springer, vol. 2(4), pages 369-397.
    6. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
    7. 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.
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    Cited by:

    1. Yingjia Guo, 2014. "The Stability of Solutions for a Fractional Predator‐Prey System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Shu-Li Mei, 2014. "Faber‐Schauder Wavelet Sparse Grid Approach for Option Pricing with Transactions Cost," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Tong Wang & Pingping Zhao & Aimin Song, 2022. "Power Option Pricing Based on Time‐Fractional Model and Triangular Interval Type‐2 Fuzzy Numbers," Complexity, John Wiley & Sons, vol. 2022(1).
    4. Paula Morales-Bañuelos & Sebastian Elias Rodríguez Bojalil & Luis Alberto Quezada-Téllez & Guillermo Fernández-Anaya, 2025. "A General Conformable Black–Scholes Equation for Option Pricing," Mathematics, MDPI, vol. 13(10), pages 1-29, May.
    5. Manzoor Ahmad & Rajshree Mishra & Renu Jain, 2025. "Time Fractional Black–Scholes Model and Its Solution Through Sumudu Transform Iterative Method," Computational Economics, Springer;Society for Computational Economics, vol. 66(5), pages 4199-4218, November.
    6. Jaspreet Kaur & Srinivasan Natesan, 2026. "Numerical Solution of Time-Fractional Black–Scholes PDE by Non-symmetric Interior Penalty Galerkin Method," Computational Economics, Springer;Society for Computational Economics, vol. 67(2), pages 685-708, February.

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