Contract options are the most important part of an investment strategy. An option is a contract that entitles the owner or holder to sell an asset on a designated maturity date. A binary or asset-or-nothing option is an option in which the option holder will perform or not the option. There are many methods used in determining the option contract value, one of this is the Monte Carlo Quasi method of the Faure random. The purpose of this study is to determine the value of binary type option contract using the Quasi Monte Carlo method of the Faure random and compare with the Monte Carlo method. The results of this study indicate that the option contract calculated by the Monte Carlo Quasi method results in a more fair value. Monte Carlo method simulation 10.000 generate  standard error is 0.9316 and the option convergence at 18.9144. While Quasi Monte Carlo simulation  3000 generate standard error is 0.09091 and the option convergence at 18.8203. This show  the  Quasi Monte Carlo method reaches a faster convergent of Monte Carlo method.