UM
Circulant preconditioning technique for barrier options pricing under fractional diffusion models
Wenfei Wang; Xu Chen; Deng Ding; Siu-Long Lei
2015-09-02
Source PublicationInternational Journal of Computer Mathematics
ISSN0020-7160
Volume92Issue:12Pages:2596-2614
Abstract

In recent years, considerable literature has proposed the more general class of exponential Lévy processes as the underlying model for prices of financial quantities, which thus better explain many important empirical facts of financial markets. Finite moment log stable, Carr–Geman–Madan–Yor and KoBoL models are chosen from those above-mentioned models as the dynamics of underlying equity prices in this paper. With such models pricing barrier options, one kind of financial derivatives is transformed to solve specific fractional partial differential equations (FPDEs). This study focuses on numerically solving these FPDEs via the fully implicit scheme, with the shifted Grünwald approximation. The circulant preconditioned generalized minimal residual method which converges very fast with theoretical proof is incorporated for solving resultant linear systems. Numerical examples are given to demonstrate the effectiveness of the proposed preconditioner and show the accuracy of our method compared with that done by the Fourier cosine expansion method as a benchmark.

KeywordBarrier Options Pricing Circulant Preconditioner Fractional Diffusion Equations Krylov Subspace Methods Lévy Process
DOI10.1080/00207160.2015.1077948
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000363753800014
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Cited Times [WOS]:17   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Personal research not belonging to the institution
Corresponding AuthorSiu-Long Lei
AffiliationDepartment of Mathematics, University of Macau, Macao,China
First Author AffilicationUniversity of Macau
Corresponding Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Wenfei Wang,Xu Chen,Deng Ding,et al. Circulant preconditioning technique for barrier options pricing under fractional diffusion models[J]. International Journal of Computer Mathematics,2015,92(12):2596-2614.
APA Wenfei Wang,Xu Chen,Deng Ding,&Siu-Long Lei.(2015).Circulant preconditioning technique for barrier options pricing under fractional diffusion models.International Journal of Computer Mathematics,92(12),2596-2614.
MLA Wenfei Wang,et al."Circulant preconditioning technique for barrier options pricing under fractional diffusion models".International Journal of Computer Mathematics 92.12(2015):2596-2614.
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