The Approximate Analytic Solution of the Time-Fractional Black-Scholes Equation with a European Option Based on the Katugampola Fractional Derivative [PDF]
Mathematics, 2021 In the finance market, it is well known that the price change of the underlying fractal transmission system can be modeled with the Black-Scholes equation.
Sivaporn Ampun, Panumart Sawangtong
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Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type [PDF]
Computation, 2021 In the finance market, the Black–Scholes equation is used to model the price change of the underlying fractal transmission system. Moreover, the fractional differential equations recently are accepted by researchers that fractional differential equations
Sirunya Thanompolkrang +2 more
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Compact Difference Schemes with Temporal Uniform/Non-Uniform Meshes for Time-Fractional Black–Scholes Equation [PDF]
Fractal and Fractional, 2023 In this paper, we are interested in the effective numerical schemes of the time-fractional Black–Scholes equation. We convert the original equation into an equivalent integral-differential equation and then discretize the time-integral term in the ...
Jie Gu, Lijuan Nong, Qian Yi, An Chen
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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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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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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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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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An Efficient Numerical Scheme for a Time-Fractional Black–Scholes Partial Differential Equation Derived from the Fractal Market Hypothesis [PDF]
Fractal and FractionalSince the early 1970s, the study of Black–Scholes (BS) partial differential equations (PDEs) under the Efficient Market Hypothesis (EMH) has been a subject of active research in financial engineering.
Samuel M. Nuugulu +2 more
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Galerkin-finite difference method for fractional parabolic partial differential equations [PDF]
MethodsXThe fractional form of the classical diffusion equation embodies the super-diffusive and sub-diffusive characteristics of any flow, depending on the fractional order. This study aims to approximate the solution of parabolic partial differential equations
Md. Shorif Hossan +2 more
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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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