On the ϵ-Approximation of the Solution of the Black-Scholes Equation

Amnuay Kananthai

Abstract

In this paper, we study the well known equation named the Black-Scholes equation. Normally, it is so complicate to find the solution of the Black-Scholes equation which is the option prices directly. But in this work we use the ϵ-approximation to find such option prices and also obtained the interesting kernel related to the interest rate  r and the volatility of the stock s. Moreover, we obtained the boundedness of the option price in the Sobolev space by giving the suitable initial condition on such option price.