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

Date

2020-11-01

Author

Kozpınar, Sinem
Karasözen, Bülent

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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.

Subject Keywords

Heston model, European option, American option, Discontinuous Galerkin method, Rannacher smoothing, Preconditioning

URI

https://hdl.handle.net/11511/31819
https://arxiv.org/pdf/1606.08381.pdf

Journal

MATHEMATICS AND COMPUTERS IN SIMULATION

DOI

https://doi.org/10.1016/j.matcom.2020.05.022

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

S. Kozpınar and B. Karasözen, “Pricing European and American options under Heston model using discontinuous Galerkin finite elements,” MATHEMATICS AND COMPUTERS IN SIMULATION, pp. 568–587, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31819.