A 2nd-order FDM for a 2D fractional black-scholes equation

Chen, W.; Wang, Song

doi:10.1007/978-3-319-57099-0_5

Access Status

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Authors

Chen, W.

Wang, Song

Date

2017

Type

Conference Paper

Metadata

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Citation

Chen, W. and Wang, S. 2017. A 2nd-order FDM for a 2D fractional black-scholes equation, pp. 46-57.

Source Title

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

DOI

10.1007/978-3-319-57099-0_5

ISBN

9783319570983

School

Department of Mathematics and Statistics

URI

http://hdl.handle.net/20.500.11937/55150

Collection

Curtin Research Publications

Abstract

© Springer International Publishing AG 2017. We develop a finite difference method (FDM) for a 2D fractional Black-Scholes equation arising in the optimal control problem of pricing European options on two assets under two independent geometric Lévy processes. We establish the convergence of the method by showing that the FDM is consistent, stable and monotone. We also show that the truncation error of the FDM is of 2nd order. Numerical experiments demonstrate that the method produces financially meaningful results when used for solving practical problems.