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Quadratic finite element and preconditioning methods for options pricing in the SVCJ model
Zhang Y.-Y.4; Pang H.-K.2; Feng L.1; Jin X.-Q.3
2014-03-01
Source PublicationJournal of Computational Finance
ABS Journal Level1
ISSN17552850 14601559
Volume17Issue:3Pages:3-30
Abstract

We consider option pricing problems in the stochastic volatility jump diffusion model with correlated and contemporaneous jumps (SVCJ) in both the return and variance processes. The option value function solves a partial integro-differential equation (PIDE). We discretize this PIDE in space by the quadratic finite element (FE) method and integrate the resulting ordinary differential equation in time using an implicit–explicit Euler-based extrapolation scheme. The coefficient matrix of the resulting linear systems is block pentadiagonal with pentadiagonal blocks. The preconditioned biconjugate gradient stabilized (PBiCGSTAB) method is used to solve the linear systems. According to the structure of the coefficient matrix, several preconditioners are implemented and compared. The performance of preconditioning techniques for solving block tridiagonal systems resulting from the linear FE discretization of the PIDE is also investigated. The combination of the quadratic FE for spatial discretization, the extrapolation scheme for time discretization and the PBiCGSTAB method with an appropriate preconditioner is found to be very efficient for solving the option pricing problems in the SVCJ model. Compared with the standard second-order linear FE method combined with the popular successive over-relaxation (SOR) linear system solver, the proposed method reduces computational time by about a factor of 20 at the accuracy level of 1% and by more than fifty times at the accuracy level of 0.1% for the barrier option example tested in the paper.

KeywordJump Diffusion-processes Stochastic Volatility American Options Returns Systems Assets
DOI10.21314/JCF.2014.287
URLView the original
Indexed BySCI
Language英语
WOS Research AreaBusiness & Economics
WOS SubjectBusiness, Finance
WOS IDWOS:000342877500002
PublisherINCISIVE MEDIA
Fulltext Access
Citation statistics
Cited Times [WOS]:2   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionDEPARTMENT OF MATHEMATICS
Affiliation1.University of Illinois at Urbana-Champaign
2.Xuzhou Normal University
3.Universidade de Macau
4.Chongqing University
Recommended Citation
GB/T 7714
Zhang Y.-Y.,Pang H.-K.,Feng L.,et al. Quadratic finite element and preconditioning methods for options pricing in the SVCJ model[J]. Journal of Computational Finance,2014,17(3):3-30.
APA Zhang Y.-Y.,Pang H.-K.,Feng L.,&Jin X.-Q..(2014).Quadratic finite element and preconditioning methods for options pricing in the SVCJ model.Journal of Computational Finance,17(3),3-30.
MLA Zhang Y.-Y.,et al."Quadratic finite element and preconditioning methods for options pricing in the SVCJ model".Journal of Computational Finance 17.3(2014):3-30.
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