Pindza, EdsonPatidar, Kailash C.Ngounda, Edgard2018-01-222018-01-222013Pindza, 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 – 2931068-9613http://hdl.handle.net/10566/3408In 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.enThis 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.pdfEuropean optionsButterfly spread optionsDigital optionsBlack-Scholes equationBarycentric interpolationImplicit-explicit predictor-corrector methodsArticle