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

Abstract

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.