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An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models
Chen,Xu1,2; Ding,Deng2; Lei,Siu Long2; Wang,Wenfei3,4
2020
Source PublicationNumerical Algorithms
ISSN1017-1398
AbstractRecently, fractional partial differential equations have been widely applied in option pricing problems, which better explains many important empirical facts of financial markets, but rare paper considers the multi-state options pricing problem based on fractional diffusion models. Thus, multi-state European option pricing problem under regime-switching tempered fractional partial differential equation is considered in this paper. Due to the expensive computational cost caused by the implicit finite difference scheme, a novel implicit-explicit finite difference scheme has been developed with consistency, stability, and convergence guarantee. Since the resulting coefficient matrix equals to the direct sum of several Toeplitz matrices, a preconditioned direct method has been proposed with O(S̄ Nlog N+ S̄ N) operation cost on each time level with adaptability analysis, where S̄ is the number of states and N is the number of grid points. Related numerical experiments including an empirical example have been presented to demonstrate the effectiveness and accuracy of the proposed numerical method.
KeywordDirect method Implicit-explicit finite difference method Multi-state European options pricing Precondition Tempered fractional partial differential equation
DOI10.1007/s11075-020-00994-7
URLView the original
Language英语
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Document TypeJournal article
CollectionUniversity of Macau
Affiliation1.School of Economics and Commerce,Guangdong University of Technology,Guangzhou,China
2.Department of Mathematics,University of Macau,Macao
3.Equity Investments and Trading Department,Haitong Securities Co.,Ltd.,Shanghai,China
4.Antai College of Economics and Management,Shanghai Jiao Tong University,Shanghai,China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Chen,Xu,Ding,Deng,Lei,Siu Long,et al. An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models[J]. Numerical Algorithms,2020.
APA Chen,Xu,Ding,Deng,Lei,Siu Long,&Wang,Wenfei.(2020).An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models.Numerical Algorithms.
MLA Chen,Xu,et al."An implicit-explicit preconditioned direct method for pricing options under regime-switching tempered fractional partial differential models".Numerical Algorithms (2020).
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