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


Xu X., Aghdam Y. E., Farnam B., Jafari H., Masetshaba M. T., ÜNLÜ C.

Fractals, vol.30, no.5, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30 Issue: 5
  • Publication Date: 2022
  • Doi Number: 10.1142/s0218348x22401661
  • Journal Name: Fractals
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Compendex, INSPEC, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Two-Dimensional Spatial-Fractional Black-Scholes Equation, Temporal-Discretization, Option Pricing, Chebyshev Basis, Spectral Method, PENALTY METHOD, AMERICAN, APPROXIMATION
  • Istanbul University Affiliated: Yes

Abstract

© 2022 The Author(s).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.