A 2nd-order ADI finite difference method for a 2D fractional Black–Scholes equation governing European two asset option pricing

doi:10.1016/j.matcom.2019.10.016

Details of Research Outputs

Title	A 2nd-order ADI finite difference method for a 2D fractional Black–Scholes equation governing European two asset option pricing
Creator	Chen，Wen 1; Wang，Song 2,3
Date Issued	2020-05-01
Source Publication	Mathematics and Computers in Simulation
ISSN	0378-4754
Volume	171 Pages:279-293
Abstract	Prices of options on two assets following two independent geometric Lévy processes are governed by a 2D fractional Black–Scholes (BS) equation. The discretization of the BS equation yields linear systems with dense system matrices and the numerical solution of them is computationally intensive. In this work, we develop a 2nd-order Crank–Nicolson Alternating Direction Implicit (ADI) method for solving these systems, based on a 2nd-order finite different technique proposed by us. A convergence theory for the method is established. Numerical results are presented to demonstrate the theoretical convergent rate of the ADI method and its computational efficiency.
Keyword	Alternating direction implicit method Finite difference Option pricing Two-dimensional spatial-fractional Black–Scholes equation
DOI	10.1016/j.matcom.2019.10.016
URL	View source
Language	英语English
Scopus ID	2-s2.0-85078741762
Citation statistics	Cited Times:26[WOS] [WOS Record] [Related Records in WOS]
Document Type	Journal article
Identifier	http://repository.uic.edu.cn/handle/39GCC9TT/12714
Collection	Research outside affiliated institution
Corresponding Author	Wang，Song
Affiliation	1.DATA61,The Commonwealth Scientific and Industrial Research Organisation,DocklandsVIC 3008,34 Village Street,Australia 2.Department of Mathematics & Statistics,Curtin University,Perth,GPO Box U1987,WA 6845,Australia 3.Shenzhen Audencia Business School,WeBank Institute of Fintech,Guangdong Laboratory of Artificial Intelligence and Digital Economy (SZ),Shenzhen University,Shenzhen,518060,China
Recommended Citation GB/T 7714	Chen，Wen,Wang，Song. A 2nd-order ADI finite difference method for a 2D fractional Black–Scholes equation governing European two asset option pricing[J]. Mathematics and Computers in Simulation, 2020, 171: 279-293.
APA	Chen，Wen, & Wang，Song. (2020). A 2nd-order ADI finite difference method for a 2D fractional Black–Scholes equation governing European two asset option pricing. Mathematics and Computers in Simulation, 171, 279-293.
MLA	Chen，Wen,et al."A 2nd-order ADI finite difference method for a 2D fractional Black–Scholes equation governing European two asset option pricing". Mathematics and Computers in Simulation 171(2020): 279-293.

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