Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform

Elbeleze, Asma Ali; Kılıçman, Adem; Taib, Bachok M.

doi:10.1155/2013/524852

Cited by 64 publications

(55 citation statements)

References 30 publications

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“…For example, these techniques have been used to evaluate the performance of an electrical resistance inductance and capacitance (RLC) circuit using a new fractional operator with a local and nonlocal kernel [1], to price fractional European vanilla-type options [2,3], to analyze a new model of H1N1 spread [4], to model the population growth [5], to apply the homotopy analysis method [6], the Adomian decomposition method [7,8], the homotopy perturbation method [9,10], He's variational iteration method in conformable derivative sense [11], the generalized differential transform method [12], the finite difference method [13] and the multivariate Padé approximation method [14]. Moreover, these proposed fractional techniques have been used to obtain the solution of the optimal control problem [15], the constrained optimization problem [16], the portfolio optimization problem [17], the diffusion-wave problem [18], etc.…”

Section: Introduction and Some Preliminariesmentioning

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: Introduction and Some Preliminariesmentioning

confidence: 99%

“…For example, [9,31,32] are relatively new approaches providing an analytical and numerical approximation to the Black-Scholes option pricing equation. The financial system can be viewed as money, capital and derivative markets (options, futures, forwards, swaps, etc.).…”

Section: Introduction and Some Preliminariesmentioning

confidence: 99%

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

2018

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“…E represents the expiration price of the option. The fractional BSOPE has been examined with the help of various techniques such as Laplace Transform Method (LTM) [10], Homotopy Perturbation Method (HPM) [11], Homotopy Analysis Method (HAM) [11], Sumudu Transform Method (STM) [12], Projected Differential Transformation Method (PDTM) [13],…”

Section: Introductionmentioning

confidence: 99%

A new iterative method based solution for fractional Black–Scholes option pricing equations (BSOPE)

Jena

2018

SN Appl. Sci.

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In this manuscript, a new expansion technique namely residual power series method is used for finding the analytical solution of the Fractional Black-Scholes equation with an initial condition for European option pricing problem. The Black-Scholes formula is important for estimating European call and put option on a non-dividend paying stock in particular when it contains time-fractional derivatives. The fractional derivative is defined in Caputo sense. This technique is based on fractional power series expansion. The convergence analysis of the present method is also deliberated. Example problems are given to examine the efficacy of the proposed method. Obtained solutions are compared with exact solutions solved by other techniques which demonstrate that the present method is robust and easy to implement for other fractional problems arising in science and engineering.

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“…Recently, Sumudu transform is adopted in some famous analytical methods [16,17,18], the combination of Sumudu transform and homotopy perturbation method is used to simplify the solution process and improve the solution's accuracy.…”

Section: Introductionmentioning

confidence: 99%

A New Iterational Method for Ordinary Equations Using Sumudu Transform

Li¹,

Chen²

2016

AAN

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A novel modification of the variational iteration method (VIM) is proposed by means of the Sumudu transform. This approach is a universal way to identify the multiplier, which is simple and effective, and successfully extended to ordinary differential equations, including the nonlinear and variable coefficient ones. The Lagrange multiplier can be easily identified by the Sumudu transform and the nonlinear term will be handled by the Adomian series. Examples are given to elucidate the process and the reliability of the method.

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Homotopy Perturbation Method for Fractional Black-Scholes European Option Pricing Equations Using Sumudu Transform

Cited by 64 publications

References 30 publications

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

A new iterative method based solution for fractional Black–Scholes option pricing equations (BSOPE)

A New Iterational Method for Ordinary Equations Using Sumudu Transform

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