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Analysis of fractional differential equation and its application to realistic data

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  • Aljethi, Reem Abdullah
  • Kılıçman, Adem

Abstract

This paper aims to propose a new a Fractional differential equation which derived from the classical Lévy model by introducing new parameters in order to fit the realistic data. The model is based on a combination of generalized tempered stable (GTS) process and Lévy stable process (LSP). A numerical method is chosen to solve the fractional partial differential equation associated to Fractional Lévy Stochastic model. Then, using the accurate information collected from the Yahoo Finance, the inverse approach is applied to estimate the unknown parameters for the Fractional Lévy stochastic model. Finally, numerical results are presented and a conclusion is drawn.

Suggested Citation

  • Aljethi, Reem Abdullah & Kılıçman, Adem, 2023. "Analysis of fractional differential equation and its application to realistic data," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003478
    DOI: 10.1016/j.chaos.2023.113446
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    References listed on IDEAS

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    1. Svetlana I. Boyarchenko & Sergei Z. Levendorskiǐ, 2000. "Option Pricing For Truncated Lévy Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 549-552.
    2. 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.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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