Results 71 to 80 of about 17,205,246 (164)

An interior penalty method for a parabolic complementarity problem involving a fractional Black-Scholes operator

Journal of Inequalities and Applications
In this paper, an interior penalty method is proposed to solve a parabolic complementarity problem involving fractional Black–Scholes operator arising in pricing American options under a geometric Lévy process.
Yarui Duan, Song Wang, Yuying Zhou, Leijun Zhu   +3 more
doaj   +1 more source

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   +1 more source

Physics-informed neural networks for the fractional Fokker–Planck equation in a Heston-type stochastic volatility model with time-dependent parameters

Machine Learning with Applications
This work presents a physics-informed neural network framework for solving the time-fractional Fokker–Planck equation governing the joint probability density of asset price and stochastic volatility in a Heston-type model with fully time-dependent ...
Muhammed Ahmed Ibrahim, Tamirat Temesgen Dufera, Sileshi Mebrate   +2 more
doaj   +1 more source

Novel Approaches for Getting the Solution of the Fractional Black–Scholes Equation Described by Mittag-Leffler Fractional Derivative

, 2020
The value of an option plays an important role in finance. In this paper, we use the Black–Scholes equation, which is described by the nonsingular fractional-order derivative, to determine the value of an option. We propose both a numerical scheme and an
Awa Traoré, Babacar Sène, Ndolane Sene, Seydou Nourou Ndiaye   +3 more
core   +1 more source

Bayesian Analysis of the Black-Scholes Option Price [PDF]

, 2004
This paper investigates the statistical properties of the Black-Scholes option price under a Bayesian approach. We incorporate randomness, both in the price process and in volatility, to derive the prior and posterior densities of a European call option.

core   +2 more sources

Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation [PDF]

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs.
Michel Fournié, Ansgar Jüngel, Bertram Düring   +2 more
core  

Galerkin approach by certain shifted Jacobi polynomials for solving the time-fractional Black-Scholes equation

Boundary Value Problems
This work presents a spectral Galerkin approach for solving the time-fractional Black-Scholes equation (TFBSE) used in option pricing models, considering memory effects. We use certain shifted Jacobi polynomials as the basis functions.
A. G. Atta, M. A. Abdelkawy, Anna Napoli, W. M. Abd-Elhameed   +3 more
doaj   +1 more source

Optimal Algebras and Novel Solutions of Time-Fractional 2+1−D European Call Option Model

Discrete Dynamics in Nature and Society
In this article, we analyse the time-fractional 2+1−D Black–Scholes model for European call options by employing Lie symmetry analysis. We derive the infinitesimal transformations and classify the optimal systems.
Gimnitz Simon S., B. Bira, Sathiyaraj Thambiayya   +2 more
doaj   +1 more source

Approximate Analytical Solution of the Black–Scholes Model with Two Assets Based on the ABC Time-Fractional Derivative

Axioms
The classical Black–Scholes model assumes Markovian dynamics and cannot capture the long-range dependence and gradual memory decay observed in real markets.
Kamonchat Trachoo, Inthira Chaiya, Din Prathumwan   +2 more
doaj   +1 more source

Numerically pricing American and European options using a time fractional Black–Scholes model in financial decision-making

Alexandria Engineering Journal
The time fractional Black–Scholes equation (TFBSE) is designed to evaluate price fluctuations within a correlated fractal transmission system. This model prices American or European put and call options on non-dividend-paying stocks.
Omid Nikan, Jalil Rashidinia, Hossein Jafari   +2 more
doaj   +1 more source