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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, Hindawi, vol. 2013, pages 1-10, June.
    • Handle: RePEc:hin:jnlaaa:194286
    DOI: 10.1155/2013/194286
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    Cited by:

    1. Khudair, Ayad R. & Haddad, S.A.M. & khalaf, Sanaa L., 2017. "Restricted fractional differential transform for solving irrational order fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 101(C), pages 81-85.
    2. Batra, Luckshay & Taneja, H.C., 2021. "Approximate-Analytical solution to the information measure’s based quanto option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    3. Jean-Philippe Aguilar & Jan Korbel & Yuri Luchko, 2019. "Applications of the Fractional Diffusion Equation to Option Pricing and Risk Calculations," Mathematics, MDPI, vol. 7(9), pages 1-23, September.
    4. Panumart Sawangtong & Kamonchat Trachoo & Wannika Sawangtong & Benchawan Wiwattanapataphee, 2018. "The Analytical Solution for the Black-Scholes Equation with Two Assets in the Liouville-Caputo Fractional Derivative Sense," Mathematics, MDPI, vol. 6(8), pages 1-14, July.
    5. Ketelbuters, John-John & Hainaut, Donatien, 2022. "CDS pricing with fractional Hawkes processes," European Journal of Operational Research, Elsevier, vol. 297(3), pages 1139-1150.
    6. Ludmila Kirianova, 2020. "Modeling of Strength Characteristics of Polymer Concrete Via the Wave Equation with a Fractional Derivative," Mathematics, MDPI, vol. 8(10), pages 1-10, October.

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