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Pricing of American options, using the Brennan–Schwartz algorithm based on finite elements

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  • Madi, Sofiane
  • Cherif Bouras, Mohamed
  • Haiour, Mohamed
  • Stahel, Andreas

Abstract

A finite element method and implicit time steps are used to determine the price of an American option. The algorithm of Brennan and Schwartz is adapted to this situation and we prove convergence. Numerical tests confirm the theoretical result and lead to a smaller error for the same computational effort, compared to the finite difference method.

Suggested Citation

  • Madi, Sofiane & Cherif Bouras, Mohamed & Haiour, Mohamed & Stahel, Andreas, 2018. "Pricing of American options, using the Brennan–Schwartz algorithm based on finite elements," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 846-852.
    • Handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:846-852
    DOI: 10.1016/j.amc.2018.06.028
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    References listed on IDEAS

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    1. Patrick Jaillet & Damien Lamberton & Bernard Lapeyre, 1990. "Variational inequalities and the pricing of American options," Post-Print hal-01667008, HAL.
    2. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    3. 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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    Cited by:

    1. Guo, Peidong & Zhang, Jizhou & Wang, Qian, 2020. "Path-dependent game options with Asian features," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Tsvetelin S. Zaevski, 2024. "Quadratic American Strangle Options in Light of Two-Sided Optimal Stopping Problems," Mathematics, MDPI, vol. 12(10), pages 1-27, May.
    3. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

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