Results 21 to 30 of about 228 (169)

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

Solution of time fractional Black-Scholes European option pricing equation arising in financial market

Nonlinear Engineering, 2016
In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation.
Ravi Kanth A.S.V., Aruna K.
doaj   +2 more sources

Numerical computation of fractional Black–Scholes equation arising in financial market

Egyptian Journal of Basic and Applied Sciences, 2014
AbstractThe aim of present paper is to present a numerical algorithm for time-fractional Black–Scholes equation with boundary condition for a European option problem by using homotopy perturbation method and homotopy analysis method. The fractional derivative is described in the Caputo sense.
Kumar, Sunil, Kumar, Devendra, Singh, Jagdev   +2 more
openaire   +3 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

An Analysis of the Fractional-Order Option Pricing Problem for Two Assets by the Generalized Laplace Variational Iteration Approach

Fractal and Fractional, 2022
An option is the right to buy or sell a good at a predetermined price in the future. For customers or financial companies, knowing an option’s pricing is crucial.
Sivaporn Ampun, Panumart Sawangtong, Wannika Sawangtong   +2 more
doaj   +1 more source

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
doaj   +1 more source

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

Application of the Generalized Laplace Homotopy Perturbation Method to the Time-Fractional Black–Scholes Equations Based on the Katugampola Fractional Derivative in Caputo Type

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, Wannika Sawangtong, Panumart Sawangtong   +2 more
doaj   +1 more source

Option valuation in markets with finite liquidity under fractional CEV assets [PDF]

Mathematics and Modeling in Finance, 2022
‎The aim of this paper is to numerically price the European double barrier option by calculating the governing fractional Black-Scholes equation in illiquid markets‎.
Azadeh Ghasemifard, Seddigheh Banihashemi, Afshin Babaei   +2 more
doaj   +1 more source

Forecasting the behaviour of fractional Black-Scholes option pricing equation by laplace perturbation iteration algorithm

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, Mariam Sultana, Muhammad Khalid, Faheem Zaidi, Kamsing Nonlaopon   +4 more
doaj   +1 more source