Year: 2020
Author: Hongmei Zhang, Fawang Liu, Shanzhen Chen, Ming Shen
Annals of Applied Mathematics, Vol. 36 (2020), Iss. 1 : pp. 91–110
Abstract
In this paper, a two dimensional (2D) fractional Black-Scholes (FBS) model on two assets following independent geometric Lévy processes is solved numerically. A high order convergent implicit difference scheme is constructed and detailed numerical analysis is established. The fractional derivative is a quasi-differential operator, whose nonlocal nature yields a dense lower Hessenberg block coefficient matrix. In order to speed up calculation and save storage space, a fast bi-conjugate gradient stabilized (FBi-CGSTAB) method is proposed to solve the resultant linear system. Finally, one example with a known exact solution is provided to assess the effectiveness and efficiency of the presented fast numerical technique. The pricing of a European Call-on-Min option is showed in the other example, in which the influence of fractional derivative order and volatility on the 2D FBS model is revealed by comparing with the classical 2D B-S model.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2020-AAM-18094
Annals of Applied Mathematics, Vol. 36 (2020), Iss. 1 : pp. 91–110
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: 2D fractional Black-Scholes model Lévy process fractional derivative numerical simulation fast bi-conjugate gradient stabilized method.