On the ε-approximation of the solution of the Black-Scholes equation

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 εapproximation to find such option prices and also obtained the interesting kernel related to the interest rate r and the volatility fi 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. © 2013 by the Mathematical Association of Thailand. All rights reserved.