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A fast preconditioned iterative method for two-dimensional options pricing under fractional differential models
Chen,Xu1; Ding,Deng1; Lei,Siu Long1; Wang,Wenfei2,3
2020-01-15
Source PublicationComputers and Mathematics with Applications
ISSN0898-1221
Volume79Issue:2Pages:440-456
AbstractIn recent years, fractional partial differential equation (FPDE) has been widely applied in options pricing problems, which better explains many important empirical facts of financial markets. However, the vast majority of the literatures focus on pricing the single asset option under the FPDE framework. In this paper, a two-dimensional FPDE governing the valuation of rainbow options is established, where two underlying assets are assumed to follow independent exponential Lévy processes, and its boundary conditions are determined by solving one-dimensional FPDEs. A second-order accurate finite difference scheme is proposed to discretize the two-dimensional FPDE. Given the block Toeplitz with Toeplitz block structure of the coefficient matrix, a fast preconditioned Krylov subspace method is developed for solving the resulting linear system with O(NlogN) computational complexity per iteration, where N is the matrix size. The proposed preconditioner accelerates the convergence of the iterative method with theoretical analysis. Numerical examples are given to demonstrate the accuracy and efficiency of our proposed numerical methods.
KeywordFinite difference method Finite moment log stable model Preconditioner Rainbow options pricing Two-dimensional fractional partial differential equation
DOI10.1016/j.camwa.2019.07.010
URLView the original
Language英语
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Document TypeJournal article
CollectionUniversity of Macau
Corresponding AuthorWang,Wenfei
Affiliation1.Department of Mathematics,University of Macau,Macao
2.Equity Investments and Trading Department,Haitong Securities Co.,Ltd.,Shanghai,China
3.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. A fast preconditioned iterative method for two-dimensional options pricing under fractional differential models[J]. Computers and Mathematics with Applications,2020,79(2):440-456.
APA Chen,Xu,Ding,Deng,Lei,Siu Long,&Wang,Wenfei.(2020).A fast preconditioned iterative method for two-dimensional options pricing under fractional differential models.Computers and Mathematics with Applications,79(2),440-456.
MLA Chen,Xu,et al."A fast preconditioned iterative method for two-dimensional options pricing under fractional differential models".Computers and Mathematics with Applications 79.2(2020):440-456.
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