Results 21 to 30 of about 4,828 (174)

Approximation of Caputo Fractional Derivative and Numerical Solutions of Fractional Differential Equations

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, Slavi Georgiev, Venelin Todorov   +2 more
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

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, Abdullah Khamis Alzahrani, Hashim Mohammed Alshehri, Stanford Shateyi   +3 more
doaj   +1 more source

Hedging in fractional Black-Scholes model with transaction costs [PDF]

, 2017
We consider conditional-mean hedging in a fractional Black-Scholes pricing model in the presence of proportional transaction costs. We develop an explicit formula for the conditional-mean hedging portfolio in terms of the recently discovered explicit ...
Shokrollahi, Foad, Sottinen, Tommi
core   +2 more sources

Conditional-Mean Hedging Under Transaction Costs in Gaussian Models [PDF]

, 2017
We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions.
Sottinen, Tommi, Viitasaari, Lauri
core   +2 more sources

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
doaj   +1 more source

A hybrid Chelyshkov wavelet-finite differences method for time-fractional black-Scholes equation [PDF]

Journal of Mahani Mathematical Research
In this paper, a hybrid method for solving time-fractional Black-Scholes equation is introduced for option pricing. The presented method is based on time and space discretization.
Seyyed Amjad Samareh Hashemi, Habibollah Saeedi, Ali Foroush Bastani   +2 more
doaj   +1 more source

Martingale Option Pricing [PDF]

, 2007
We show that our generalization of the Black-Scholes partial differential equation (pde) for nontrivial diffusion coefficients is equivalent to a Martingale in the risk neutral discounted stock price.
Bassler, K. E., Gunaratne, G. H., McCauley, J. L.   +2 more
core   +2 more sources

Inverse Multiquadric Function to Price Financial Options under the Fractional Black–Scholes Model

Fractal and Fractional, 2022
The inverse multiquadric radial basis function (RBF), which is one of the most important functions in the theory of RBFs, is employed on an adaptive mesh of points for pricing a fractional Black–Scholes partial differential equation (PDE) based on the ...
Yanlai Song, Stanford Shateyi
doaj   +1 more source