Numerical Solution of Nonlinear Black – Scholes Equation by Accelerated Genetic Algorithm

Abstract

In this paper we using an accelerated genetic algorithm to find the numerical solution of the nonlinear versions of the standard Black–Scholes partial differential equation  with stochastic volatility (transaction coast) for European call option .  We study this equation with different models of volatility and comparison these solutions with the solution of linear model of Black-Scholes equation without transaction coast .

Keywords: Nonlinear Black-Scholes Equation , Accelerated Genetic Algorithm , Option Pricing