Estimation of the Parameters of the Stochastic Differential Equations Black-Scholes Model Share Price of Gold

Problem statement: The estimation of the parameters is one of main problems of the dynamic models in many scientific fields and particularly in economics and finance. In this study, we examine the techniques of estimation of the parameters of the Black-Scholes model. These techniques are based on the function of probability. Approach: The two estimations are based on the likelihood function. The “discret” method considers the function of density of transition from the process of diffusion normal log. The second method proposes the estimate of the parameters of the model via the observation of the time of first passage of the process through a constant limit of which the density is known. Results: One treats an application of the share price of gold. Conclusion: A comparative study between both methods of estimations of the parameters and the forecast is given.