IDEAS home Printed from https://ideas.repec.org/a/wsi/ijfexx/v05y2018i03ns2424786318500287.html
   My bibliography  Save this article

The source of error behavior for the solution of Black–Scholes PDE by finite difference and finite element methods

Author

Listed:
  • H. Ünsal Özer

    (Istanbul Technical University, Department of Mathematics, 34469 Istanbul, Turkey)

  • Ahmet Duran

    (Istanbul Technical University, Department of Mathematics, 34469 Istanbul, Turkey)

Abstract

Black–Scholes partial differential equation (PDE) is one of the most famous equations in mathematical finance and financial industry. In this study, numerical solution analysis is done for Black–Scholes PDE using finite element method with linear approach and finite difference methods. The numerical solutions are compared with Black–Scholes formula for option pricing. The numerical errors are determined for the finite element and finite difference applications to Black–Scholes PDE. We examine the error behavior and find the source of the corresponding errors under various market situations.

Suggested Citation

  • H. Ünsal Özer & Ahmet Duran, 2018. "The source of error behavior for the solution of Black–Scholes PDE by finite difference and finite element methods," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 1-22, September.
    • Handle: RePEc:wsi:ijfexx:v:05:y:2018:i:03:n:s2424786318500287
    DOI: 10.1142/S2424786318500287
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S2424786318500287
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S2424786318500287?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. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893, January.
    2. 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)

    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. Yonggu Kim & Keeyoung Shin & Joseph Ahn & Eul-Bum Lee, 2017. "Probabilistic Cash Flow-Based Optimal Investment Timing Using Two-Color Rainbow Options Valuation for Economic Sustainability Appraisement," Sustainability, MDPI, vol. 9(10), pages 1-16, October.
    2. Kenji Hamatani & Masao Fukushima, 2011. "Pricing American options with uncertain volatility through stochastic linear complementarity models," Computational Optimization and Applications, Springer, vol. 50(2), pages 263-286, October.
    3. Tobias Lipp & Grégoire Loeper & Olivier Pironneau, 2013. "Mixing Monte-Carlo and Partial Differential Equations for Pricing Options," Post-Print hal-01558826, HAL.
    4. Otto Konstandatos & Timothy J Kyng, 2012. "Real Options Analysis for Commodity Based Mining Enterprises with Compound and Barrier Features," Published Paper Series 2012-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    5. Marco Realdon, 2006. "Valuation of the Firm's Liabilities when Equity Holders are also Creditors," Discussion Papers 06/16, Department of Economics, University of York.
    6. P. Pellizzari, 1998. "Efficient Monte Carlo Pricing of Basket Options," Finance 9801001, University Library of Munich, Germany.
    7. Kwamie Dunbar, . "An Empirical Review of United States Corporate Default Swap Valuation: The Implications of Functional Forms," Fordham Economics Dissertations, Fordham University, Department of Economics, number 2005.2.
    8. Hitoshi Imai & Naoyuki Ishimura & Ikumi Mottate & Masaaki Nakamura, 2006. "On the Hoggard–Whalley–Wilmott Equation for the Pricing of Options with Transaction Costs," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(4), pages 315-326, December.
    9. Khaliq, A.Q.M. & Voss, D.A. & Kazmi, S.H.K., 2006. "A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 489-502, February.
    10. Michael A. Kouritzin, 2016. "Explicit Heston Solutions and Stochastic Approximation for Path-dependent Option Pricing," Papers 1608.02028, arXiv.org, revised Apr 2018.
    11. Ben Boukai, 2020. "How Much Is Your Strangle Worth? On the Relative Value of the Strangle under the Black-Scholes Pricing Model," Applied Economics and Finance, Redfame publishing, vol. 7(4), pages 138-146, July.
    12. Ziwei Ke & Joanna Goard, 2019. "Penalty American Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-32, March.
    13. Tomas Bokes, 2010. "A unified approach to determining the early exercise boundary position at expiry for American style of general class of derivatives," Papers 1012.0348, arXiv.org, revised Mar 2011.
    14. Schachter, J.A. & Mancarella, P., 2016. "A critical review of Real Options thinking for valuing investment flexibility in Smart Grids and low carbon energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 56(C), pages 261-271.
    15. Sivaporn Ampun & Panumart Sawangtong, 2021. "The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
    16. Deswal, Komal & Kumar, Devendra, 2022. "Rannacher time-marching with orthogonal spline collocation method for retrieving the discontinuous behavior of hedging parameters," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    17. Ömür Ugur, 2008. "An Introduction to Computational Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number p556, February.
    18. Marco Realdon, 2007. "Valuation of the Firm's Liabilities When Equity Holders Are Also Creditors," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 34(5‐6), pages 950-975, June.
    19. Gong, Pu & He, Zhiwei & Zhu, Song-Ping, 2006. "Pricing convertible bonds based on a multi-stage compound-option model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 449-462.
    20. C. E. Dangerfield & A. E. Whalley & N. Hanley & C. A. Gilligan, 2018. "What a Difference a Stochastic Process Makes: Epidemiological-Based Real Options Models of Optimal Treatment of Disease," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 70(3), pages 691-711, July.

    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:wsi:ijfexx:v:05:y:2018:i:03:n:s2424786318500287. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscientific.com/worldscinet/ijfe .

    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.