Implicit-explicit predictor-corrector methods combined with improved spectral methods for pricing European style vanilla and exotic options

dc.contributor.authorPindza, Edson
dc.contributor.authorPatidar, Kailash C.
dc.contributor.authorNgounda, Edgard
dc.date.accessioned2018-01-22T13:19:46Z
dc.date.available2018-01-22T13:19:46Z
dc.date.issued2013
dc.description.abstractIn this paper we present a robust numerical method to solve several types of European style option pricing problems. The governing equations are described by variants of Black-Scholes partial differential equations (BS-PDEs) of the reaction-diffusion-advection type. To discretise these BS-PDEs numerically, we use the spectral methods in the asset (spatial) direction and couple them with a third-order implicit-explicit predictor-corrector (IMEX-PC) method for the discretisation in the time direction. The use of this high-order time integration scheme sustains the better accuracy of the spectral methods for which they are well-known. Our spectral method consists of a pseudospectral formulation of the BS-PDEs by means of an improved Lagrange formula. On the other hand, in the IMEX-PC methods, we integrate the diffusion terms implicitly whereas the reaction and advection terms are integrated explicitly. Using this combined approach, we first solve the equations for standard European options and then extend this approach to digital options, butterfly spread options, and European calls in the Heston model. Numerical experiments illustrate that our approach is highly accurate and very efficient for pricing financial options such as those described above.en_US
dc.identifier.citationPindza, E. et al. (2013). Implicit-explicit predictor-corrector methods combined with improved spectral methods for pricing European style vanilla and exotic options. Electronic Transactions on Numerical Analysis, 40: 268 – 293en_US
dc.identifier.issn1068-9613
dc.identifier.urihttp://hdl.handle.net/10566/3408
dc.language.isoenen_US
dc.privacy.showsubmitterFALSE
dc.publisherKent State Universityen_US
dc.rightsThis is the author-version of the article that was published online at: http://etna.math.kent.edu/vol.40.2013/pp268-293.dir/pp268-293.pdf
dc.status.ispeerreviewedTRUE
dc.subjectEuropean optionsen_US
dc.subjectButterfly spread optionsen_US
dc.subjectDigital optionsen_US
dc.subjectBlack-Scholes equationen_US
dc.subjectBarycentric interpolationen_US
dc.subjectImplicit-explicit predictor-corrector methodsen_US
dc.titleImplicit-explicit predictor-corrector methods combined with improved spectral methods for pricing European style vanilla and exotic optionsen_US
dc.typeArticleen_US

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