Results 21 to 30 of about 4,852 (158)

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

Novel ANN Method for Solving Ordinary and Time-Fractional Black–Scholes Equation

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   +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

An adaptive moving mesh method for a time-fractional Black–Scholes equation

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   +1 more source

A robust numerical solution to a time-fractional Black–Scholes equation

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   +1 more source

Numerical Solution of Fractional Black-Scholes Equation by Using Radial Basis Function (RBF) Approximation Method

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, Ali R. Siheili, A. Neisy   +2 more
doaj  

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

Long memory stochastic volatility in option pricing

, 2004
The aim of this paper is to present a simple stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black-Scholes equation involving volatility with long-range dependence.
Fedotov, Sergei, Tan, Abby
core   +4 more sources

Efficient operator splitting and spectral methods for the time-space fractional Black–Scholes equation

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
doaj   +1 more source

Using a Mix of Finite Difference Methods and Fractional Differential Transformations to Solve Modified Black–Scholes Fractional Equations

Mathematics
This paper discusses finding solutions to the modified Fractional Black–Scholes equation. As is well known, the options theory is beneficial in the stock market.
Agus Sugandha, Endang Rusyaman, Sukono, Ema Carnia   +3 more
doaj   +1 more source