A Robust Spectral Method for Solving Heston’s Model

E. Ngounda (), K. C. Patidar () and E. Pindza ()
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E. Ngounda: University of the Western Cape
K. C. Patidar: University of the Western Cape
E. Pindza: University of the Western Cape

Journal of Optimization Theory and Applications, 2014, vol. 161, issue 1, No 9, 164-178

Abstract: Abstract In 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).

Keywords: Heston’s volatility model; Spectral methods; Laplace transform; Stochastic volatility (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/s10957-013-0284-x

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