PRICING EUROPEAN TWO-ASSET OPTION USING THE SPECTRAL METHOD WITH SECOND-KIND CHEBYSHEV POLYNOMIALS

Xianhua Xu, Yones Esmaeelzade Aghdam, Behnaz Farnam, Hossein Jafari, Mantepu Tshepo Masetshaba and ÜNLÜ Canan
Additional contact information
Xianhua Xu: College of Business, City University of Hong Kong, Hong Kong, P. R. China
Yones Esmaeelzade Aghdam: ��Department of Mathematics, 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
Mantepu Tshepo Masetshaba: ��Department of Decision Sciences, University of South Africa, UNISA0003, South Africa
ÜNLÜ Canan: *Mathematics Department, Science Faculty, İstanbul University, 34134 Vezneciler, Fatih/İstanbul, Turkey

FRACTALS (fractals), 2022, vol. 30, issue 05, 1-8

Abstract: The path of the Lévy process can be considered for prices of options such as a Rainbow or Basket option on two assets which leads to a 2D Black–Scholes model. The generalized model of this type of equation can be referred to as a 2D spatial-fractional Black–Scholes equation. The analytical solution of this kind is very complex and difficult and can even be said to be unattainable. For this reason, a numerical method has been proposed to solve it via the collocation method based on the Chebyshev orthogonal basis. Moreover, based on the derivatives in the called model, we approximated the derivative operator by using this type of base. Then we first obtained the temporal discrete form and finally the full-discrete form and turned it into a system of linear equations with the help of Chebyshev base roots.

Keywords: Two-Dimensional Spatial-Fractional Black–Scholes Equation; Temporal-Discretization; Option Pricing; Chebyshev Basis; Spectral Method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22401661

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