Ngounda, E.Patidar, Kailash C.Pindza, E.2017-12-042017-12-042014Egounda, E. et al. (2014). A robust spectral method for solving Heston’s model. Journal of Optimization Theory and Application, 161: 164 – 1780022-3239http://dx.doi.org/10.1007/s10957-013-0284-xhttp://hdl.handle.net/10566/3294In this paper, we consider the Heston’s volatility model (Heston in Rev. Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the spectral collocation method and the Laplace transforms method. To approximate the two dimensional PDE, we construct a grid which is the tensor product of the two grids, each of which is based on the Chebyshev points in the two spacial directions. The resulting semi-discrete problem is then solved by applying the Laplace transform method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA J. Appl. Math. 23(1): 97–120, 1979).enThis is the author-version of the article published online at: http://dx.doi.org/10.1007/s10957-013-0284-xHeston’s volatility modelSpectral methodsLaplace transformStochastic volatilityArticle