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Fractal Fract 2018, 2(1), 3; https://doi.org/10.3390/fractalfract2010003

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

1
Department of Mathematics-Computer Sciences, Faculty of Science, Necmettin Erbakan University, Konya 42090, Turkey
2
Department of Mathematics, Faculty of Sciences and Arts, Balıkesir University, Balıkesir 10145, Turkey
*
Author to whom correspondence should be addressed.
Received: 28 December 2017 / Revised: 14 January 2018 / Accepted: 14 January 2018 / Published: 16 January 2018
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering)
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Abstract

Recently, fractional differential equations (FDEs) have attracted much more attention in modeling real-life problems. Since most FDEs do not have exact solutions, numerical solution methods are used commonly. Therefore, in this study, we have demonstrated a novel approximate-analytical solution method, which is called the Laplace homotopy analysis method (LHAM) using the Caputo–Fabrizio (CF) fractional derivative operator. The recommended method is obtained by combining Laplace transform (LT) and the homotopy analysis method (HAM). We have used the fractional operator suggested by Caputo and Fabrizio in 2015 based on the exponential kernel. We have considered the LHAM with this derivative in order to obtain the solutions of the fractional Black–Scholes equations (FBSEs) with the initial conditions. In addition to this, the convergence and stability analysis of the model have been constructed. According to the results of this study, it can be concluded that the LHAM in the sense of the CF fractional derivative is an effective and accurate method, which is computable in the series easily in a short time. View Full-Text
Keywords: fractional option pricing problem; Caputo–Fabrizio fractional derivative; homotopy analysis method; Laplace transform fractional option pricing problem; Caputo–Fabrizio fractional derivative; homotopy analysis method; Laplace transform
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Yavuz, M.; Özdemir, N. European Vanilla Option Pricing Model of Fractional Order without Singular Kernel. Fractal Fract 2018, 2, 3.

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