Lie symmetry analysis of a fractional Black-Scholes equation [PDF]
AIP Conference Proceedings, 2019 In 2000, Walter Wyss looked into the fractional version of the Black-Scholes equation for the first time. He gave a solution of the fractional Black-Scholes equation by using the Greens function [14].
Chong, Kam Yoon, O'Hara, John G
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A universal difference method for time-space fractional Black-Scholes equation [PDF]
Advances in Difference Equations, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sun Shuzhen +3 more
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Novel ANN Method for Solving Ordinary and Time-Fractional Black–Scholes Equation [PDF]
Complexity, 2021 The main aim of this study is to introduce a 2-layered artificial neural network (ANN) for solving the Black–Scholes partial differential equation (PDE) of either fractional or ordinary orders.
Saeed Bajalan, Nastaran Bajalan
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A robust numerical solution to a time-fractional Black–Scholes equation [PDF]
Advances in Difference Equations, 2021 Dividend paying European stock options are modeled using a time-fractional Black–Scholes (tfBS) partial differential equation (PDE). The underlying fractional stochastic dynamics explored in this work are appropriate for capturing market fluctuations in ...
S. M. Nuugulu, F. Gideon, K. C. Patidar
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Lie Symmetries and the Invariant Solutions of the Fractional Black–Scholes Equation under Time-Dependent Parameters [PDF]
Fractal and FractionalIn this paper, we consider the time-fractional Black–Scholes model with deterministic, time-varying coefficients. These time parametric constituents produce a model with greater flexibility that may capture empirical results from financial markets and ...
Sameerah Jamal +2 more
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Analytical solution of time-fractional N-dimensional Black-Scholes equation using LHPM
Ratio Mathematica, 2023 A famous Black-Scholes differential equation is used for pricing options in financial world which represents financial derivatives more significantly. Option is one of the crucial financial derivatives. Sawangtong P., Trachoo K., Sawangtong W.
Sanjay Ghevariya, CHETANBHAI PATEL
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Spectral Solutions for Fractional Black–Scholes Equations [PDF]
Mathematical Problems in Engineering, 2022 This paper presents a numerical method to solve accurately the fractional Black–Scholes model of pricing evolution. A fully spectral collocation technique for the two independent variables is derived. The shifted fractional Jacobi–Gauss–Radau and shifted fractional Jacobi–Gauss–Lobatto collocation techniques are utilized.
M. A. Abdelkawy, António M. Lopes
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An adaptive moving mesh method for a time-fractional Black–Scholes equation [PDF]
Advances in Difference Equations, 2019 In this paper we study the numerical method for a time-fractional Black–Scholes equation, which is used for option pricing. The solution of the fractional-order differential equation may be singular near certain domain boundaries, which leads to ...
Jian Huang, Zhongdi Cen, Jialiang Zhao
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Results in Applied Mathematics, 2021 In this paper, we aim at developing improved L1 operator splitting method and spectral method for Black–Scholes differential systems with fractional derivatives in both time and space.
Mustafa Almushaira, Feng Chen, Fei Liu
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Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation [PDF]
Journal of Function Spaces, 2021 In this study, we present an accurate and efficient nonuniform finite difference method for the three-dimensional (3D) time-fractional Black–Scholes (BS) equation.
Sangkwon Kim +5 more
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