Results 11 to 20 of about 4,903 (187)

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
doaj   +3 more sources

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
doaj   +3 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

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
doaj   +3 more sources

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

Fractal and Fractional
The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of
Hongmei Zhang, Mengchen Zhang, Fawang Liu, Ming Shen   +3 more
doaj   +2 more sources

The Numerical Solution of Fractional Black-Scholes-Schrodinger Equation Using the RBFs Method [PDF]

Advances in Mathematical Physics, 2020
In this paper, radial basis functions (RBFs) method was used to solve a fractional Black-Scholes-Schrodinger equation in an option pricing of financial problems. The RBFs method is applied in discretizing a spatial derivative process.
Naravadee Nualsaard, Anirut Luadsong, Nitima Aschariyaphotha   +2 more
doaj   +3 more sources

Efficient High-Accuracy Numerical Scheme for the Solution of Time Fractional Parabolic Partial Differential Equations With Application in Financial Modeling

Journal of Mathematics
Parabolic partial equations, particularly the Black–Scholes equation, are fundamental in mathematical finance for option pricing and risk management. Despite their widespread use, efficiently solving these equations remains a challenge, especially in ...
Hadis Azin, Ali Iloon Kashkooly
doaj   +2 more sources

Analysis of a Finite Difference Method for a Time-Fractional Black–Scholes Equation

Fractal and Fractional
The 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, Chaobao Huang, Tao Sun, Hu Chen   +3 more
doaj   +2 more sources

Spectral Solutions for Fractional Black–Scholes Equations

Mathematical Problems in Engineering, 2022
This paper presents a numerical method to solve accurately the fractional Black–Scholes model of pricing evolution. A fully spectral collocation technique for the two independent variables is derived. The shifted fractional Jacobi–Gauss–Radau and shifted fractional Jacobi–Gauss–Lobatto collocation techniques are utilized.
M. A. Abdelkawy, António M. Lopes
openaire   +1 more source

A universal difference method for time-space fractional Black-Scholes equation [PDF]

Advances in Difference Equations, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Sun Shuzhen, Wu Lifei, Yang Xiaozhong, Zhang Xue   +3 more
core   +3 more sources