A class of intrinsic parallel difference methods for time-space fractional Black–Scholes equation

Li, Yue; Yang, Xiaozhong; Sun, Shurong

doi:10.1186/s13662-018-1736-2

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…By employing parameter θ(0 ≤ θ ≤ 1), they obtained a difference scheme, known as the C-N scheme when θ = 1 2 . This work was further extended by Li et al [107]. They developed two alternative schemes, namely the explicit-implicit scheme and implicitexplicit scheme, which not only ensure numerical stability but also exhibit favorable parallel characteristics.…”

Section: Equation For Fractal Stock Exchange Dynamics and Its Solutionmentioning

confidence: 97%

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

Zhang,

Liu

et al. 2024

Fractal Fract

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The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of the B-S equation, however, relies on a set of rigorous assumptions that give rise to several limitations. The non-local property of the fractional derivative (FD) and the identification of fractal characteristics in financial markets have paved the way for the introduction and rapid development of fractional calculus in finance. In comparison to the classical B-S equation, the fractional B-S equations (FBSEs) offer a more flexible representation of market behavior by incorporating long-range dependence, heavy-tailed and leptokurtic distributions, as well as multifractality. This enables better modeling of extreme events and complex market phenomena, The fractional B-S equations can more accurately depict the price fluctuations in actual financial markets, thereby providing a more reliable basis for derivative pricing and risk management. This paper aims to offer a comprehensive review of various FBSEs for pricing European options, including associated solution techniques. It contributes to a deeper understanding of financial model development and its practical implications, thereby assisting researchers in making informed decisions about the most suitable approach for their needs.

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Section: Equation For Fractal Stock Exchange Dynamics and Its Solutionmentioning

confidence: 97%

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

Zhang,

Liu

et al. 2024

Fractal Fract

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An efficient radial basis functions mesh deformation with greedy algorithm based on recurrence Choleskey decomposition and parallel computing

Fang¹,

Yu³

et al. 2019

Journal of Computational Physics

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Solution of time-space fractional Black-Scholes European option pricing problem through fractional reduced differential transform method

Ahmad¹,

Mishra²,

Jain³

2021

Fractional Differential Calculus

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Mathematical model introduced by Black and Scholes express financial derivatives more significantly. This model with fractional derivatives resulting in fractional Black-Scholes (B-S) equation express financial problems in a better way. In this paper, we introduce the fractional reduced differential transform method (FRDTM) to solve the time-space fractional Black-Scholes equation executing European options. This method is a modified version of the original differential transform method (DTM). This method proves to be valid for solving time-space Black-Scholes equation as it reduces the computational work to a greater extent. Moreover, this method helps in finding the solution without linearization or discretization. The efficiency of the method is tested by solving certain examples. The proposed mathematical representation can be useful to understand and solve time-space fractional differential equations arising in financial mathematics and other related fields.

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A class of intrinsic parallel difference methods for time-space fractional Black–Scholes equation

Cited by 3 publications

References 20 publications

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

An efficient radial basis functions mesh deformation with greedy algorithm based on recurrence Choleskey decomposition and parallel computing

Solution of time-space fractional Black-Scholes European option pricing problem through fractional reduced differential transform method

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