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

H. Ünsal Özer () and Ahmet Duran ()
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H. Ünsal Özer: Istanbul Technical University, Department of Mathematics, 34469 Istanbul, Turkey

International Journal of Financial Engineering (IJFE), 2018, vol. 05, issue 03, 1-22

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.

Keywords: Mathematical finance; Black-Scholes partial differential equation; error analysis; finite element method; finite difference method; option pricing (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1142/S2424786318500287

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