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Revisiting Black–Scholes: A Smooth Wiener Approach to Derivation and a Self-Contained Solution

Mathematics
This study presents a self-contained derivation and solution of the Black and Scholes partial differential equation (PDE), replacing the standard Wiener process with a smoothed Wiener process, which is a differentiable stochastic process constructed via ...
Alessandro Saccal, Andrey Artemenkov
doaj   +1 more source

PT Symmetry, Non-Gaussian Path Integrals, and the Quantum Black-Scholes Equation. [PDF]

Entropy (Basel), 2019
Hicks W.
europepmc   +1 more source

An Efficient Numerical Model for the Black–Scholes Equations

Journal of Applied Mathematics
In this paper, a novel numerical model for the Black–Scholes equations is developed. To address some potential issues that may arise when solving this equation using the conventional model, the original Black–Scholes equation is reformulated as a ...
Yan Zhou, Yunxing Zhang
doaj   +1 more source

Cubic Trigonometric B-spline Collocation Approach for Black-Scholes Method

四川大学学报. 自然科学版, 2017
A cubic trigonometric B-spline collocation approach is developed for the numerical solution of Black-Scholes equation governing European option pricing.
WU Bei-Bei, YIN Jun-Feng, JIN Meng
doaj  

Symmetries of the Black-Scholes equation

, 2012
We determine the algebra of isovectors for the Black--Scholes equation.
Lescot, Paul
core   +1 more source

An unconditionally stable, positivity-preserving splitting scheme for nonlinear Black-Scholes equation with transaction costs. [PDF]

ScientificWorldJournal, 2014
Guo J, Wang W.
europepmc   +1 more source

Comparative Error Analysis of the Black-Scholes Equation [PDF]

, 2019
Finance is a rapidly growing area in our banking world today. With this ever-increasing development come more complex derivative products than simple buy-and-sell trades. Financial derivatives such as futures and options have been developed stemming from
Chen, Chuan
core  

Greek parameters of nonlinear Black-Scholes equation

, 2016
Derivatives are used in hedging European options against risks. The partial derivatives of the solution to either a variable or a parameter in the Black-Scholes model are called risk (Greek) parameters or simply the Greeks.
Esekon, Joseph E
core  

Solution to a nonlinear Black-Scholes equation

Electronic Journal of Differential Equations, 2011
Option pricing with transaction costs leads to a nonlinear Black-Scholes type equation where the nonlinear term reflects the presence of transaction costs. Under suitable conditions, we prove the existence of weak solutions in a bounded domain and we
Maria Cristina Mariani, Emmanuel Kengni Ncheuguim, Indranil SenGupta   +2 more
doaj  

Neural Network Learning of Black-Scholes Equation for Option Pricing [PDF]

One of the most discussed problems in the financial world is stock option pricing. The Black-Scholes Equation is a Parabolic Partial Differential Equation which provides an option pricing model.
Ferreira, Tiago Alessandro Espinola, Santos, Daniel de Souza   +1 more
core   +1 more source