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Article

A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities

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Department of Mathematics, Tekirdag Namik Kemal University, Degirmenalti, Tekirdag 59030, Turkey
2
Department of Business Administration, Petroleum-Gas University, Blvd. Bucuresti, no.39, 100680 Ploiesti, Romania
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Department of Mathematics, Yildiz Technical University, Istanbul 34220, Turkey
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 760; https://doi.org/10.3390/math7080760
Received: 24 July 2019 / Revised: 14 August 2019 / Accepted: 16 August 2019 / Published: 19 August 2019
(This article belongs to the Special Issue Financial Mathematics)
Since financial engineering problems are of great importance in the academic community, effective methods are still needed to analyze these models. Therefore, this article focuses mainly on capturing the discrete behavior of linear and nonlinear Black–Scholes European option pricing models. To achieve this, this article presents a combined method; a sixth order finite difference (FD6) scheme in space and a third–order strong stability preserving Runge–Kutta (SSPRK3) over time. The computed results are compared with available literature and the exact solution. The computed results revealed that the current method seems to be quite strong both quantitatively and qualitatively with minimal computational effort. Therefore, this method appears to be a very reliable alternative and flexible to implement in solving the problem while preserving the physical properties of such realistic processes. View Full-Text
Keywords: Black–Scholes equation; option pricing modelling; European option; volatility; high-order finite difference Black–Scholes equation; option pricing modelling; European option; volatility; high-order finite difference
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MDPI and ACS Style

Gulen, S.; Popescu, C.; Sari, M. A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities. Mathematics 2019, 7, 760. https://doi.org/10.3390/math7080760

AMA Style

Gulen S, Popescu C, Sari M. A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities. Mathematics. 2019; 7(8):760. https://doi.org/10.3390/math7080760

Chicago/Turabian Style

Gulen, Seda, Catalin Popescu, and Murat Sari. 2019. "A New Approach for the Black–Scholes Model with Linear and Nonlinear Volatilities" Mathematics 7, no. 8: 760. https://doi.org/10.3390/math7080760

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