Results 11 to 20 of about 178 (138)
Nonuniform Finite Difference Scheme for the Three-Dimensional Time-Fractional Black–Scholes Equation
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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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 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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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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Discrete Dynamics in Nature and Society, 2020 The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an
Ndolane Sene +3 more
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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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Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method
Abstract and Applied Analysis, 2013 This work deals with the put option pricing problems based on the time-fractional Black-Scholes equation, where the fractional derivative is a so-called modified Riemann-Liouville fractional derivative.
Lina Song, Weiguo Wang
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Novel ANN Method for Solving Ordinary and Time-Fractional Black–Scholes Equation
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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An adaptive moving mesh method for a time-fractional Black–Scholes equation
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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پژوهشهای ریاضی, 2020 Introduction Fractional Differential Calculus (FDC) began in the 17th century and its initial discussions were related to the works of Leibniz, Lagrange, Abel and others.
Sedighe Sharifian +2 more
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