Results 1 to 10 of about 3,326,697 (175)

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

Recovery of Implied Volatility in a Spatial-Fractional Black–Scholes Equation Under a Finite Moment Log Stable Model

Mathematics
In this paper, we study direct and inverse problems for a spatial-fractional Black–Scholes equation with space-dependent volatility. For the direct problem, we provide CN-WSGD (Crank–Nicholson and the weighted and shifted Grünwald difference) scheme to ...
Xiaoying Jiang, Chunmei Shi, Yujie Wei
doaj   +1 more source

Lie Symmetries and the Invariant Solutions of the Fractional Black–Scholes Equation under Time-Dependent Parameters

Fractal and Fractional
In this paper, we consider the time-fractional Black–Scholes model with deterministic, time-varying coefficients. These time parametric constituents produce a model with greater flexibility that may capture empirical results from financial markets and ...
Sameerah Jamal, Reginald Champala, Suhail Khan   +2 more
doaj   +1 more source

A New Stabled Relaxation Method for Pricing European Options Under the Time-Fractional Vasicek Model. [PDF]

Comput Econ, 2023
Kharrat M, Arfaoui H.
europepmc   +1 more source

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

Quantum effects in an expanded Black-Scholes model. [PDF]

Eur Phys J B, 2022
Bhatnagar A, Vvedensky DD.
europepmc   +1 more source

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   +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

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