Results 81 to 90 of about 3,326,698 (171)

Invariant solutions of the Black-Scholes equation [PDF]

, 2022
Dissertation (MSc (Applied Mathematics))--University of Pretoria, 2022.In this study, we discuss derivatives, Lie symmetries and invariant solutions of the Black Scholes equation.

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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

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
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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

Barrier Options and a Reflection Principle of the Fractional Brownian Motion [PDF]

The purpose of this paper is to obtain the price of the barrier options in a fractional Brownian motion environment in the special case of zero interest rate. As a consequence we derive a reflection principle for the fractional Brownian motion.fractional
Cipian Necula
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Simple Formulas to Option Pricing and Hedging in the Black- Scholes Model [PDF]

For option whose striking price equals the forward price of the underlying asset, the Black-Scholes pricing formula can be approximated in closed-form. A interesting result is that the derived equation is not only very simple in structure but also that ...
paolo pianca
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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

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