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Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements

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  • Sinem Kozp{i}nar
  • Murat Uzunca
  • Bulent Karasozen

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

  • Sinem Kozp{i}nar & Murat Uzunca & Bulent Karasozen, 2016. "Pricing European and American Options under Heston Model using Discontinuous Galerkin Finite Elements," Papers 1606.08381, arXiv.org, revised Mar 2020.
    • Handle: RePEc:arx:papers:1606.08381
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    References listed on IDEAS

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    1. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
    2. Bertram During & Michel Fourni'e & Christof Heuer, 2014. "High-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids," Papers 1404.5138, arXiv.org.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. 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.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    1. M. Khasi & J. Rashidinia, 2024. "A Bilinear Pseudo-spectral Method for Solving Two-asset European and American Pricing Options," Computational Economics, Springer;Society for Computational Economics, vol. 63(2), pages 893-918, February.

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