A contour integral method for the Black-Scholes and Heston equations

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dc.contributor.authorIn't Hout K.J.
dc.contributor.authorWeideman J.A.C.
dc.date.accessioned2011-10-13T16:58:10Z
dc.date.available2011-10-13T16:58:10Z
dc.date.issued2011
dc.description.abstractA contour integral method recently proposed by W eideman [IMA J. Numer. Anal., 30 (2010), pp. 334-350] for integrating semidiscrete advection-diffusion PDEs is improved and extended for application to some of the important equations of mathematical finance. Using estimates for the numerical range of the spatial operator, optimal contour parameters are derived theoretically and tested numerically. An improvement on the existing method is the use of Krylov methods for the shifted linear systems, the solution of which represents the major computational cost of the algorithm. A parallel implementation is also considered. Test examples presented are the Black-Scholes PDE in one space dimension and the Heston PDE in two dimensions, for both vanilla and barrier options. In the Heston case efficiency is compared to ADI splitting schemes, and experiments show that the contour integral method is superior for the range of medium to high accuracy requirements. © 2011 Society for Industrial and Applied Mathematics.
dc.description.versionArticle
dc.identifier.citationSIAM Journal on Scientific Computing
dc.identifier.citation33
dc.identifier.citation2
dc.identifier.citationhttp://www.scopus.com/inward/record.url?eid=2-s2.0-79957621114&partnerID=40&md5=cd211a425ebf204ee1a7f33e6b98cb9c
dc.identifier.issn10648275
dc.identifier.other10.1137/090776081
dc.identifier.urihttp://hdl.handle.net/10019.1/16633
dc.subjectBlack-scholes equation
dc.subjectFinancial option pricing
dc.subjectHeston equation
dc.subjectKrylov methods
dc.subjectLaplace transform
dc.subjectMatrix exponential
dc.subjectNumerical contour integration
dc.subjectParallelism
dc.subjectBlack Scholes equations
dc.subjectFinancial option pricing
dc.subjectHeston equation
dc.subjectKrylov method
dc.subjectMatrix exponential
dc.subjectNumerical contour integration
dc.subjectParallelism
dc.subjectEconomics
dc.subjectLaplace transforms
dc.subjectLinear systems
dc.subjectMathematical operators
dc.titleA contour integral method for the Black-Scholes and Heston equations
dc.typeArticle
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