Analysis of a Finite Difference Method for a Time-Fractional Black–Scholes Equation [PDF]
Fractal and FractionalThe goal of this paper is to give an error analysis of a finite difference method for a time-fractional Black–Scholes equation with weakly singular solutions.
Qingzhao Li +3 more
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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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Parameter estimation for time-fractional Black-Scholes equation with S &P 500 index option [PDF]
Numerical Algorithms, 2023 This paper aims to estimate the parameters of the time-fractional Black-Scholes (TFBS) partial differential equation with the Caputo fractional derivative by using the real option prices of the S &P 500 index options.
Xingyu An +4 more
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Solution of the Fractional Black-Scholes Option Pricing Model by Finite Difference Method [PDF]
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 [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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SOLUTIONS OF A TIME FRACTIONAL BLACK-SCHOLES EQUATION UNDER THE CONSTANT ELASTICITY OF VARIANCE PROCESS [PDF]
International Journal of Apllied Mathematics, 2023 : In this paper we consider backward problem and inverse source problem for time-fractional Black-Scholes equation, which arises from pricing double barrier option under the constant elasticity of variance process.
Kangqun Zhang
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Alexandria Engineering Journal, 2023 Trivially, the time-fractional Black–Scholes (FBS) equation is utilized to describe the behavior of the option pricing in financial markets. This work is intended as an attempt to introduce the ψ-Hilfer fractional Black–Scholes (ψ-HFBS) equation.
F. Mohammadizadeh +4 more
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