Tikhonov regularization for simultaneous inversion of initial value and source term of a time‐fractional Black‐Scholes equation [PDF]
Mathematical methods in the applied sciencesThis paper studies simultaneous inversion of initial value and source term of a time‐fractional Black‐Scholes equation. This problem is ill‐posed, and we use Tikhonov regularization method to solve it.
Hanghang Wu, Hongqi Yang
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The Source Term Inversion of a Time‐Fractional Black‐Scholes Equation by Fractional Landweber Iterative Regularization Method [PDF]
Mathematical methods in the applied sciencesThis paper studies the source term inversion of a time‐fractional Black‐Scholes equation, which is an ill‐posed problem. Under certain assumptions, we establish conditional stability results and derive the optimal error bound for the problem.
Hongqi Yang, Hongqi Yang
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CAUCHYThe classical Black-Scholes model is widely used in option pricing but relies on idealized assumptions such as constant volatility and memoryless market dynamics, which limit its accuracy in capturing real-world financial behavior.
Elza Rahma Dihna +2 more
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A compact difference scheme for time-fractional Black-Scholes equation with time-dependent parameters under the CEV model: American options [PDF]
, 2021 Maryam Rezaei +3 more
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Journal of Computational MathematicsThis paper is devoted to identifying the source term and initial value simultaneously in a time-fractional Black-Scholes equation, which is an ill-posed problem.
Shuang Yu, Hongqi Yang
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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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On the solution of two-dimensional fractional Black–Scholes equation for European put option
Advances in Difference Equations, 2020 The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order Black–Scholes equation for a European put option.
Din Prathumwan, Kamonchat Trachoo
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Fractal and Fractional, 2023 In this paper, we consider an approximation of the Caputo fractional derivative and its asymptotic expansion formula, whose generating function is the polylogarithm function.
Yuri Dimitrov +2 more
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On a Multigrid Method for Tempered Fractional Diffusion Equations
Fractal and Fractional, 2021 In this paper, we develop a suitable multigrid iterative solution method for the numerical solution of second- and third-order discrete schemes for the tempered fractional diffusion equation.
Linlin Bu, Cornelis W. Oosterlee
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Investigation of Higher Order Localized Approximations for a Fractional Pricing Model in Finance
Mathematics, 2023 In this work, by considering spatial uniform meshes and stencils having five adjacent discretization nodes, we furnish a numerical scheme to solve the time-fractional Black–Scholes (partial differential equation) PDE to price financial options under the ...
Malik Zaka Ullah +3 more
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