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
doaj +2 more sources
Laplace Decomposition Method for Solving Fractional Black-Scholes European Option Pricing Equation [PDF]
, 2020 Fractional calculus is related to derivatives and integrals with the order is not an integer. Fractional Black-Scholes partial differential equation to determine the price of European-type call options is an application of fractional calculus in the ...
Owoyemi, Abiodun Ezekiel +3 more
core +4 more sources
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
doaj +2 more sources
Numerical Solution of Fractional Black-Scholes Equation by Using Radial Basis Function (RBF) Approximation Method [PDF]
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
doaj +4 more sources
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
doaj +2 more sources
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
doaj +2 more sources
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
doaj +2 more sources
On the solution of two-dimensional fractional Black–Scholes equation for European put option [PDF]
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
doaj +2 more sources
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
doaj +2 more sources
Alexandria Engineering Journal, 2023 Financial derivatives plays a major role in all financial deals these days. Black–Scholes option pricing model gives a risk free analysis for investing in options. In the current work, a method called the Laplace Perturbation Iteration Algorithm is being
Fareeha Sami Khan +4 more
doaj +2 more sources