UM
A Fast Preconditioned Penalty Method for American Options Pricing Under Regime-Switching Tempered Fractional Diffusion Models
Siu-Long Lei1; Wenfei Wang1,2; Xu Chen1; Deng Ding1
2017-11-21
Source PublicationJournal of Scientific Computing
ISSN0885-7474
Volume75Issue:3Pages:1633-1655
Abstract

A fast preconditioned penalty method is developed for a system of parabolic linear complementarity problems (LCPs) involving tempered fractional order partial derivatives governing the price of American options whose underlying asset follows a geometry Lévy process with multi-state regime switching. By means of the penalty method, the system of LCPs is approximated with a penalty term by a system of nonlinear tempered fractional partial differential equations (TFPDEs) coupled by a finite-state Markov chain. The system of nonlinear TFPDEs is discretized with the shifted Grünwald approximation by an upwind finite difference scheme which is shown to be unconditionally stable. Semi-smooth Newton’s method is utilized to solve the finite difference scheme as an outer iterative method in which the Jacobi matrix is found to possess Toeplitz-plus-diagonal structure. Consequently, the resulting linear system can be fast solved by the Krylov subspace method as an inner iterative method via fast Fourier transform (FFT). Furthermore, a novel preconditioner is proposed to speed up the convergence rate of the inner Krylov subspace iteration with theoretical analysis. With the above-mentioned preconditioning technique via FFT, under some mild conditions, the operation cost in each Newton’s step can be expected to be O(Nlog N) , where N is the size of the coefficient matrix. Numerical examples are given to demonstrate the accuracy and efficiency of our proposed fast preconditioned penalty method.

KeywordAmerican Options Fast Preconditioned Penalty Method Linear Complementarity Problems Nonlinear Tempered Fractional Partial Differential Equations Regime-switching Lévy Process Unconditional Stability
DOI10.1007/s10915-017-0602-9
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000431399600018
Fulltext Access
Citation statistics
Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Personal research not belonging to the institution
Affiliation1.Department of Mathematics, University of Macau, Macau, China
2.Shenwan Hongyuan Securities Postdoctoral Research Station, Shanghai, China
First Author AffilicationUniversity of Macau
Recommended Citation
GB/T 7714
Siu-Long Lei,Wenfei Wang,Xu Chen,et al. A Fast Preconditioned Penalty Method for American Options Pricing Under Regime-Switching Tempered Fractional Diffusion Models[J]. Journal of Scientific Computing,2017,75(3):1633-1655.
APA Siu-Long Lei,Wenfei Wang,Xu Chen,&Deng Ding.(2017).A Fast Preconditioned Penalty Method for American Options Pricing Under Regime-Switching Tempered Fractional Diffusion Models.Journal of Scientific Computing,75(3),1633-1655.
MLA Siu-Long Lei,et al."A Fast Preconditioned Penalty Method for American Options Pricing Under Regime-Switching Tempered Fractional Diffusion Models".Journal of Scientific Computing 75.3(2017):1633-1655.
Files in This Item:
There are no files associated with this item.
Related Services
Recommend this item
Bookmark
Usage statistics
Export to Endnote
Google Scholar
Similar articles in Google Scholar
[Siu-Long Lei]'s Articles
[Wenfei Wang]'s Articles
[Xu Chen]'s Articles
Baidu academic
Similar articles in Baidu academic
[Siu-Long Lei]'s Articles
[Wenfei Wang]'s Articles
[Xu Chen]'s Articles
Bing Scholar
Similar articles in Bing Scholar
[Siu-Long Lei]'s Articles
[Wenfei Wang]'s Articles
[Xu Chen]'s Articles
Terms of Use
No data!
Social Bookmark/Share
All comments (0)
No comment.
 

Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.