scholarly journals Error Analysis of Meshfree Approximation in Nonlinear Black-Scholes Model

2020 ◽  
pp. 55-63
Author(s):  
Godwin Onwona-Agyeman ◽  
Francis T. Oduro ◽  
Gabriel Asare Okyere ◽  
Awudu Obeng
Keyword(s):  
Error Analysis ◽  
Radial Basis Function ◽  
Numerical Method ◽  
Transaction Cost ◽  
Basis Function ◽  
Cost Model ◽  
Meshfree Approximation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Radial Basis

The transaction cost model of Guy Barles and Halil Mete Soner is incorporated into the standard Black Scholes Equation. The resulting model is solved by a numerical method, called, the meshfree approximation using radial basis function. The errors produced by the scheme are discussed and presented in diagrams and tables.

scholarly journals Radial Basis Function in Nonlinear Black-Scholes Option Pricing Equation with Transaction Cost

2019 ◽  
pp. 1-11
Author(s):  
Godwin Onwona-Agyeman ◽  
Francis T. Oduro
Keyword(s):  
Differential Equations ◽  
Radial Basis Function ◽  
Basis Function ◽  
Numerical Technique ◽  
Option Price ◽  
Meshfree Approximation ◽  
Black Scholes Model ◽  
Black Scholes ◽  
The World ◽  
Radial Basis

Differential equations play significant role in the world of finance since most problems in these areas are modeled by differential equations. Majority of these problems are sometimes nonlinear and are normally solved by the use of numerical methods. This work takes a critical look at Nonlinear Black-Scholes model with special reference to the model by Guy Barles and Halil Mete Soner. The resulting model is a nonlinear Black-Scholes equation in which the variable volatility is a function of the second derivative of the option price. The nonlinear equation is solved by a special class of numerical technique, called, the meshfree approximation using radial basis function. The numerical results are presented in diagrams and tables.

scholarly journals Accurate radial basis functions technique for competitive and efficient solutions of non-linear Black-Scholes equations

2020 ◽  
Vol 20 (4) ◽  
pp. 60-83
Author(s):  
Vinícius Magalhães Pinto Marques ◽  
Gisele Tessari Santos ◽  
Mauri Fortes
Keyword(s):  
Radial Basis Function ◽  
Basis Function ◽  
Efficient Solutions ◽  
Basis Functions ◽  
Adaptive Scheme ◽  
Call Options ◽  
Black Scholes ◽  
Non Linear ◽  
Radial Basis ◽  
Complex Models

ABSTRACTObjective: This article aims to solve the non-linear Black Scholes (BS) equation for European call options using Radial Basis Function (RBF) Multi-Quadratic (MQ) Method.Methodology / Approach: This work uses the MQ RBF method applied to the solution of two complex models of nonlinear BS equation for prices of European call options with modified volatility. Linear BS models are also solved to visualize the effects of modified volatility.  Additionally, an adaptive scheme is implemented in time based on the Runge-Kutta-Fehlberg (RKF) method.

Sign in / Sign up

Export Citation Format

Share Document