Studies in option pricing have became more important and challenging in financial area because option valuation can add significant information to the decision making process. In this study we attempt to establish the American and European call option. Call option gives the buyer the right, but not the obligation to buy a specified stock at a predetermined price on or before a predetermined date. An American option may be exercised earlier before the expiration date. For European options, early exercise is not possible. It can only be exercised only at maturity. In this paper, we do mathematical experiments to solve the problem of financial valuation using Mathematica.