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

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  • 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
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    References listed on IDEAS

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    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.
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