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Boundary value methods with the Crank-Nicolson preconditioner for pricing options in the jump-diffusion model
Shu-Ling Yang1; Spike T. Lee2; Hai-Wei Sun2
2011-05-01
Source PublicationInternational Journal of Computer Mathematics
ISSN00207160 10290265
Volume88Issue:8Pages:1730-1748
Abstract

Under a jump-diffusion process, the option pricing function satisfies a partial integro-differential equation. A fourth-order compact scheme is used to discretize the spatial variable of this equation. The boundary value method is then utilized for temporal integration because of its unconditional stability and high-order accuracy. Two approaches, the local mesh refinement and the start-up procedure with refined step size, are raised to avoid the numerical malfunction brought by the nonsmooth payoff function. The GMRES method with a preconditioner which comes from the Crank-Nicolson formula is employed to solve the resulting large-scale linear system. Numerical experiments demonstrate the efficiency of the proposed method when pricing European and double barrier call options in the jump-diffusion model.

KeywordBoundary Value Method Crank-nicolson Time-marching Scheme Fourth-order Compact Scheme Jump-diffusion Preconditioner Toeplitz Matrix
DOIhttps://doi.org/10.1080/00207160.2010.524929
URLView the original
Indexed BySCI
Language英语
WOS Research AreaMathematics, Applied
WOS SubjectMathematics, Applied
WOS IDWOS:000290252400012
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Cited Times [WOS]:4   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Affiliation1.School of Applied Mathematics, Guangdong University of Technology, Guangzhou, China
2.Department of Mathematics, University of Macau, Macao, China
Recommended Citation
GB/T 7714
Shu-Ling Yang,Spike T. Lee,Hai-Wei Sun. Boundary value methods with the Crank-Nicolson preconditioner for pricing options in the jump-diffusion model[J]. International Journal of Computer Mathematics,2011,88(8):1730-1748.
APA Shu-Ling Yang,Spike T. Lee,&Hai-Wei Sun.(2011).Boundary value methods with the Crank-Nicolson preconditioner for pricing options in the jump-diffusion model.International Journal of Computer Mathematics,88(8),1730-1748.
MLA Shu-Ling Yang,et al."Boundary value methods with the Crank-Nicolson preconditioner for pricing options in the jump-diffusion model".International Journal of Computer Mathematics 88.8(2011):1730-1748.
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