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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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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A posteriori grid method for a time-fractional Black-Scholes equation
AIMS Mathematics, 2022 In this paper, a posteriori grid method for solving a time-fractional Black-Scholes equation governing European options is studied. The possible singularity of the exact solution complicates the construction of the discretization scheme for the time ...
Zhongdi Cen, Jian Huang , Aimin Xu
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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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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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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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Networks and Heterogeneous Media, 2023 In this paper, two high-order compact difference schemes with graded meshes are proposed for solving the time-fractional Black-Scholes equation. We first eliminate the convection term in the equivalent form of the considered equation by using exponential
Jie Gu, Lijuan Nong, Qian Yi, An Chen
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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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Galerkin approach by certain shifted Jacobi polynomials for solving the time-fractional Black-Scholes equation [PDF]
Boundary Value ProblemsThis work presents a spectral Galerkin approach for solving the time-fractional Black-Scholes equation (TFBSE) used in option pricing models, considering memory effects. We use certain shifted Jacobi polynomials as the basis functions.
A. G. Atta +3 more
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A high-order and fast scheme with variable time steps for the time-fractional Black-Scholes equation [PDF]
Mathematical methods in the applied sciences, 2021 In this paper, a high‐order and fast numerical method is investigated for the time‐fractional Black‐Scholes equation. In order to deal with the typical weak initial singularity of the solution, we construct a finite difference scheme with variable time ...
Kerui Song, Pin Lyu
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