A different approach to the European option pricing model with new fractional operator

Yavuz, Mehmet; Özdemir, Necati

doi:10.1051/mmnp/2018009

Cited by 82 publications

(59 citation statements)

References 35 publications

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“…Moreover, as α decreases, the payoff of the option increases. When α = 0.25, we observe that the option is overpriced [38]. The fractional model suggested in this study can model the price of different financial derivatives like swaps, warrant, etc.…”

Section: Discussionmentioning

confidence: 99%

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European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

2018

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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.

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Section: Discussionmentioning

confidence: 99%

“…As α decreases, the payoff of the option increases. When α = 0.25, we observe that the option is overpriced [38]. …”

Section: Fractional European Option Pricing Problem In the Sense Of Tmentioning

confidence: 96%

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

2018

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“…In the last two years, many authors used Caputo-Fabrizio fractional derivative operator in many interesting models and with many known methods, see [11][12][13][14][15][16][17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative

Evirgen

Yavuz

2018

ITM Web Conf.

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In this study, a fractional mathematical model with steepest descent direction is proposed to find optimal solutions for a class of nonlinear programming problem. In this sense, Caputo-Fabrizio derivative is adapted to the mathematical model. To demonstrate the solution trajectory of the mathematical model, we use the multistage variational iteration method (MVIM). Numerical simulations and comparisons on some test problems show that the mathematical model generated using Caputo-Fabrizio fractional derivative is both feasible and efficient to find optimal solutions for a certain class of equality constrained optimization problems.

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“…Recently, [14][15][16] recommended a new derivative operator namely "conformable" (CDO) and some applications of this operator in various fields have been improved. In this context, some researchers [5,7,[17][18][19][20] applied the conformable operator to solve the problems in engineering, finance, biology, medicine, physics and applied mathematics. In this study, we have solved the linear/nonlinear fractional Cauchy problem with the proposed q-HAM described by using the conformable operator.…”

Section: Introductionmentioning

confidence: 99%

On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative

Yavuz

Özdemir

2018

ITM Web Conf.

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In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.

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A different approach to the European option pricing model with new fractional operator

Cited by 82 publications

References 35 publications

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

An Alternative Approach for Nonlinear Optimization Problem with Caputo - Fabrizio Derivative

On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative

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