THE NUMERICAL STRATEGY OF TEMPERED FRACTIONAL DERIVATIVE IN EUROPEAN DOUBLE BARRIER OPTION

Chengxuan Xie, Xiaoxiao Xia, Yones Esmaeelzade Aghdam, Behnaz Farnam, Hossein Jafari and Shuchun Wang
Additional contact information
Chengxuan Xie: Department of Economics, College and Graduate School of Arts & Sciences, Boston University, Boston, USA
Xiaoxiao Xia: ��Business College, Guangzhou College of Technology and Business, Guangzhou, P. R. China
Yones Esmaeelzade Aghdam: ��Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran 16785-136, Iran
Behnaz Farnam: �Department of Mathematics, Faculty of Science, Qom University of Technology, Qom, Iran
Hossein Jafari: �Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa∥Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 110122, Taiwan
Shuchun Wang: *School of Economics, Tianjin University of Commerce, Tianjin, P. R. China

FRACTALS (fractals), 2022, vol. 30, issue 01, 1-10

Abstract: The usage of Lévy processes involving big moves or jumps over a short period of time has proven to be a successful strategy in financial analysis to capture such rare or extreme events of stock price dynamics. Models that follow the Lévy process are FMLS, Kobol, and CGMY models. Such simulations steadily raise the attention of researchers in science because of the certain best options they produce. Thus, the issue of resolving these three separate styles has gained more interest. In the new paper, we introduce the computational method of such models. At first, the left and right tempered fractional derivative with arbitrary order is approximated by using the basis function of the shifted Chebyshev polynomials of the third kind (SCPTK). In the second point, by implementing finite difference approximation, we get the semi-discrete structure to solve the tempered fractional B–S model (TFBSM). We show that this system is stable and 𠒪(δτ) is the convergence order. In practice, the processing time and the calculation time per iteration will be reduced by a quickly stabilized system. Then we use SCPTK to approximate the spatial fractional derivative to get the full design. Finally, two numerical examples are provided to illustrate the established system’s reliability and effectiveness.

Keywords: Left and Right Tempered Fractional Derivative; Chebyshev Polynomials; Convergence; Stability (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22400497

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