UM
Preconditioned iterative methods for fractional diffusion models in finance
Qing-Jiang Meng1; Deng Ding2; Qin Sheng3
2014-12-16
Source PublicationNumerical Methods for Partial Differential Equations
ISSN0749-159X
Volume31Issue:5Pages:1382-1395
Abstract

Most recent qualitative models for financial assets assume that the dynamics of underlying equity prices follows a jump or Lévy process. It has been evident that some most intricate characteristics of such dynamics can be captured by CGMY and KoBoL procedures. The prices of financial derivatives with such models satisfy fractional partial differential equations or partial integro-differential equations. This study focuses at aforementioned fractional equations and discretizes them via a monotone Crank-Nicolson procedure. A spatial extrapolation strategy is introduced to ensure an overall second-order accuracy in approximations. Preconditioned conjugate gradient normal residual methods are incorporated for solving resulted linear systems. Numerical examples are given to illustrate the accuracy and efficiency of the novel computational approaches implemented.

KeywordCrank-nicolson Discretization Fast Fourier Transform Fractional Partial Derivatives Lévy Process Preconditioning Method Toeplitz Matrix
DOI10.1002/num.21948
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000358730000002
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Cited Times [WOS]:13   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionUniversity of Macau
Personal research not belonging to the institution
Corresponding AuthorQing-Jiang Meng
Affiliation1.Post-Doctoral Research Center, China Investment Securities,Shenzhen,China
2.Department of Mathematics, University of Macau,Macao,China
3.Department of Mathematics, Center for Astrophysics, Space Physics and Engineering Research, Baylor University,Waco,76798-7328,United States
Recommended Citation
GB/T 7714
Qing-Jiang Meng,Deng Ding,Qin Sheng. Preconditioned iterative methods for fractional diffusion models in finance[J]. Numerical Methods for Partial Differential Equations,2014,31(5):1382-1395.
APA Qing-Jiang Meng,Deng Ding,&Qin Sheng.(2014).Preconditioned iterative methods for fractional diffusion models in finance.Numerical Methods for Partial Differential Equations,31(5),1382-1395.
MLA Qing-Jiang Meng,et al."Preconditioned iterative methods for fractional diffusion models in finance".Numerical Methods for Partial Differential Equations 31.5(2014):1382-1395.
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