This chapter will mainly discuss the Black Scholes model, which is applied in this research. The history of Black Scholes will be introduced, followed by the history of the equation of geometric Brownian motion. Besides these two, we will also briefly explain the financial application of gold stock price. 2.2 Gold Stock Price Shahriar Shafiee (2010) is concerned about the global gold market and gold price forecast. He said that in practice, the price and production behavior of gold differs from that of most other mineral commodities. During the 2008 financial crisis, the price of gold rose 6%, while the prices of many key minerals fell and other stocks fell around 40%. The unique and diversified nature of the demand and supply of gold is not strongly correlated with developments in other financial assets. It had concluded that the gold supply showed that approximately 160,000 tonnes of gold had been mined throughout history until the end of 2008. The demand for gold from jewelry, industrial and central banks are equivalent to approximately 100,000, 30,000 and 30,000 tonnes respectively. A significant proportion of gold demand is attributed to jewelry, which in turn can be injected on the supply side. There are a number of different price modeling methods that have been discussed in the financial literature. Geometric Brownian motion and mean reversion are two classic approaches that form the basis of some newer methods, such as stochastic price forecasting and mean reversion diffusion models. These models focus on historical price movements and a random term to estimate future prices. They do not take into account price jumps or falls in the models (Shahriar Shafiee, 2010).2.3 Black Scholes Option Pricing ModelIn the research done by Arend (2008) on the emergence of Blac.... .. middle of paper..... We devoted our study to applying statistical methods to stochastic differential equations, initially to estimate them by the historical method, which uses the property of independence and normality of the outputs. The Black-Scholes model and its alternatives are widely used by professionals. For this, the estimation of its parameters deserves attention to other more suitable techniques: discrete method. The discrete method makes it possible to estimate the parameters of the Black-Scholes model in the case of discrete paths. In this method, it is necessary to observe the process for a certain time interval, that is, to use all observations of the paths. The discrete method being based on the criterion which minimizes the variances of the estimators and the small errors with the true values ​​of the gold price (Khaldi Khaled, 2010).