A robust and accurate finite difference method for a generalized Black–Scholes equation

Cen, Zhongdi; Le, Anbo

doi:10.1016/j.cam.2011.01.018

Cited by 83 publications

(65 citation statements)

References 13 publications

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“…Cen and Le in [13] consider a numerical method based on central difference spatial discretization on a piecewise uniform mesh and an implicit time stepping technique for generalized Black-Scholes equation. In [14], Mosneagu and Dura apply numerical methods based on finite differences for solving Black-Scholes equation.…”

Section: T DX T G T X T Dt G T X T Dw T Rmentioning

confidence: 99%

Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

Edeki

Ugbebor

Owoloko

2015

Entropy

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Abstract:In this paper, a proposed computational method referred to as Projected Differential Transformation Method (PDTM) resulting from the modification of the classical Differential Transformation Method (DTM) is applied, for the first time, to the Black-Scholes Equation for European Option Valuation. The results obtained converge faster to their associated exact solution form; these easily computed results represent the analytical values of the associated European call options, and the same algorithm can be followed for European put options. It is shown that PDTM is more efficient, reliable and better than the classical DTM and other semi-analytical methods since less computational work is involved. Hence, it is strongly recommended for both linear and nonlinear stochastic differential equations (SDEs) encountered in financial mathematics.

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Section: T DX T G T X T Dt G T X T Dw T Rmentioning

confidence: 99%

Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

Edeki

Ugbebor

Owoloko

2015

Entropy

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“…In this example, let the given below generalized fractional Black-Scholes option pricing equation [10] defined as:…”

Section: Examplementioning

confidence: 99%

“…Many partial differential equations of fractional order have been studied and solved. For example many researchers studied the existence of solutions of the Black-Scholes model using many methods [8][9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

European Option Pricing of Fractional Black-Scholes Model Using Sumudu Transform and its Derivatives

Khan¹,

Ansari²

2016

GLM

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“…In addition to this, Cen and Le (2011) obtained the generalized fractional Black-Scholes equation [36] (GFBSE) by considering r = 0.06 and σ = 0.4 (2 + sin x) in Equation (2):…”

Section: Introduction and Some Preliminariesmentioning

confidence: 99%

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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A robust and accurate finite difference method for a generalized Black–Scholes equation

Cited by 83 publications

References 13 publications

Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

Analytical Solutions of the Black–Scholes Pricing Model for European Option Valuation via a Projected Differential Transformation Method

European Option Pricing of Fractional Black-Scholes Model Using Sumudu Transform and its Derivatives

European Vanilla Option Pricing Model of Fractional Order without Singular Kernel

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