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Pricing European and American options under Heston model using discontinuous Galerkin finite elements

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  • Kozpınar, Sinem
  • Uzunca, Murat
  • Karasözen, Bülent

Abstract

This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundary conditions are illustrated for European vanilla options, digital call and American put options. The convection dominated Heston model for vanishing volatility is efficiently solved utilizing the adaptive dGFEM. For fast solution of the linear complementary problem of the American options, a projected successive over relaxation (PSOR) method is developed with the norm preconditioned dGFEM. We show the efficiency and accuracy of dGFEM for option pricing by conducting comparison analysis with other methods and numerical experiments.

Suggested Citation

  • Kozpınar, Sinem & Uzunca, Murat & Karasözen, Bülent, 2020. "Pricing European and American options under Heston model using discontinuous Galerkin finite elements," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 568-587.
    • Handle: RePEc:eee:matcom:v:177:y:2020:i:c:p:568-587
    DOI: 10.1016/j.matcom.2020.05.022
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    1. Maryam Safaei & Abodolsadeh Neisy & Nader Nematollahi, 2018. "New Splitting Scheme for Pricing American Options Under the Heston Model," Computational Economics, Springer;Society for Computational Economics, vol. 52(2), pages 405-420, August.
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    9. Ballestra, Luca Vincenzo & Pacelli, Graziella, 2013. "Pricing European and American options with two stochastic factors: A highly efficient radial basis function approach," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1142-1167.
    10. Reza Mollapourasl & Ali Fereshtian & Michèle Vanmaele, 2019. "Radial Basis Functions with Partition of Unity Method for American Options with Stochastic Volatility," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 259-287, January.
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