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A Computational Method Based on the Moving Least-Squares Approach for Pricing Double Barrier Options in a Time-Fractional Black–Scholes Model

Author

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  • Ahmad Golbabai

    (Iran University of Science and Technology)

  • Omid Nikan

    (Iran University of Science and Technology)

Abstract

The mathematical modeling in trade and finance issues is the key purpose in the computation of the value and considering option during preferences in contract. This paper investigates the pricing of double barrier options when the price change of the underlying is considered as a fractal transmission system. Due to the outstanding memory effect present in the fractional derivatives, approximating financial options with regards to their hereditary characteristics can be well interpreted and stated. Motivated by the reason mentioned, relatively reliable and also efficient numerical approaches have to be found while facing with fractional differential equations. The main objective of the current paper is to obtain the approximation solution of the time fractional Black–Scholes model of order $$0

Suggested Citation

  • Ahmad Golbabai & Omid Nikan, 2020. "A Computational Method Based on the Moving Least-Squares Approach for Pricing Double Barrier Options in a Time-Fractional Black–Scholes Model," Computational Economics, Springer;Society for Computational Economics, vol. 55(1), pages 119-141, January.
    • Handle: RePEc:kap:compec:v:55:y:2020:i:1:d:10.1007_s10614-019-09880-4
    DOI: 10.1007/s10614-019-09880-4
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    1. Taghipour, M. & Aminikhah, H., 2022. "A spectral collocation method based on fractional Pell functions for solving time–fractional Black–Scholes option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Jugal Mohapatra & Sudarshan Santra & Higinio Ramos, 2024. "Analytical and Numerical Solution for the Time Fractional Black-Scholes Model Under Jump-Diffusion," Computational Economics, Springer;Society for Computational Economics, vol. 63(5), pages 1853-1878, May.
    3. M. Khasi & J. Rashidinia, 2024. "A Bilinear Pseudo-spectral Method for Solving Two-asset European and American Pricing Options," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 893-918, February.
    4. Donghyun Kim & Ji-Hun Yoon, 2023. "Analytic Method for Pricing Vulnerable External Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1561-1591, April.
    5. Changhong Guo & Shaomei Fang & Yong He, 2023. "Derivation and Application of Some Fractional Black–Scholes Equations Driven by Fractional G-Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1681-1705, April.
    6. Chaeyoung Lee & Soobin Kwak & Youngjin Hwang & Junseok Kim, 2023. "Accurate and Efficient Finite Difference Method for the Black–Scholes Model with No Far-Field Boundary Conditions," Computational Economics, Springer;Society for Computational Economics, vol. 61(3), pages 1207-1224, March.
    7. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    8. Saadet Eskiizmirliler & Korhan Günel & Refet Polat, 2021. "On the Solution of the Black–Scholes Equation Using Feed-Forward Neural Networks," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 915-941, October.
    9. M. Rezaei & A. R. Yazdanian & A. Ashrafi & S. M. Mahmoudi, 2022. "Numerically Pricing Nonlinear Time-Fractional Black–Scholes Equation with Time-Dependent Parameters Under Transaction Costs," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 243-280, June.
    10. Abdi, N. & Aminikhah, H. & Sheikhani, A.H. Refahi, 2022. "High-order compact finite difference schemes for the time-fractional Black-Scholes model governing European options," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    11. Y. Esmaeelzade Aghdam & H. Mesgarani & A. Amin & J. F. Gómez-Aguilar, 2024. "An Efficient Numerical Scheme to Approach the Time Fractional Black–Scholes Model Using Orthogonal Gegenbauer Polynomials," Computational Economics, Springer;Society for Computational Economics, vol. 64(1), pages 211-224, July.
    12. Y. Esmaeelzade Aghdam & H. Mesgarani & A. Adl & B. Farnam, 2023. "The Convergence Investigation of a Numerical Scheme for the Tempered Fractional Black-Scholes Model Arising European Double Barrier Option," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 513-528, February.
    13. Xin-Jiang He & Sha Lin, 2022. "An Analytical Approximation Formula for Barrier Option Prices Under the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 60(4), pages 1413-1425, December.
    14. 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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