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

KOZPINAR S., UZUNCA M., KARASÖZEN B.

MATHEMATICS AND COMPUTERS IN SIMULATION, vol.177, pp.568-587, 2020 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 177
  • Publication Date: 2020
  • Doi Number: 10.1016/j.matcom.2020.05.022
  • Journal Name: MATHEMATICS AND COMPUTERS IN SIMULATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH
  • Page Numbers: pp.568-587
  • Middle East Technical University Affiliated: Yes

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.