IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v339y2018icp846-852.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318305174
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.06.028?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Zaevski, Tsvetelin S., 2020. "Discounted perpetual game call options," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Darae Jeong & Minhyun Yoo & Changwoo Yoo & Junseok Kim, 2019. "A Hybrid Monte Carlo and Finite Difference Method for Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 111-124, January.
    2. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
    3. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    4. Ballestra, Luca Vincenzo & Cecere, Liliana, 2016. "A numerical method to estimate the parameters of the CEV model implied by American option prices: Evidence from NYSE," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 100-106.
    5. Riccardo Fazio, 2015. "A Posteriori Error Estimator for a Front-Fixing Finite Difference Scheme for American Options," Papers 1504.04594, arXiv.org.
    6. Leisen, Dietmar P. J., 1998. "Pricing the American put option: A detailed convergence analysis for binomial models," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1419-1444, August.
    7. Karel in 't Hout & Jari Toivanen, 2015. "Application of Operator Splitting Methods in Finance," Papers 1504.01022, arXiv.org.
    8. Pressacco, Flavio & Gaudenzi, Marcellino & Zanette, Antonino & Ziani, Laura, 2008. "New insights on testing the efficiency of methods of pricing and hedging American options," European Journal of Operational Research, Elsevier, vol. 185(1), pages 235-254, February.
    9. Mark Broadie & Jérôme Detemple, 1996. "American Options on Dividend-Paying Assets," CIRANO Working Papers 96s-16, CIRANO.
    10. Muthuraman, Kumar, 2008. "A moving boundary approach to American option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3520-3537, November.
    11. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    12. Giandomenico, Rossano, 2006. "Valuing an American Put Option," MPRA Paper 20082, University Library of Munich, Germany.
    13. Engstrom, Malin & Norden, Lars, 2000. "The early exercise premium in American put option prices," Journal of Multinational Financial Management, Elsevier, vol. 10(3-4), pages 461-479, December.
    14. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    15. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.
    16. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    17. Oleksandr Zhylyevskyy, 2010. "A fast Fourier transform technique for pricing American options under stochastic volatility," Review of Derivatives Research, Springer, vol. 13(1), pages 1-24, April.
    18. Hadjiyannakis, Steve & Culumovic, Louis & Welch, Robert L., 1998. "The relative mispricing of the constant variance American put model," International Review of Economics & Finance, Elsevier, vol. 7(2), pages 149-171.
    19. Luca Vincenzo Ballestra, 2018. "Fast and accurate calculation of American option prices," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 399-426, November.
    20. Qianru Shang & Brian Byrne, 2021. "American option pricing: Optimal Lattice models and multidimensional efficiency tests," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(4), pages 514-535, April.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:339:y:2018:i:c:p:846-852. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.