Parameter estimation is a powerful and adaptable framework that addresses the inherent complexities and uncertainties of financial data. We provide an overview of likelihood functions, and likelihood estimations, as well as the essential numerical approximations and techniques. In the financial domain, where unpredictable and non-stationary market dynamics prevail, parameter estimations of relevant SDE models prove highly relevant. We delve into practical applications, showcasing how SDEs can effectively capture the inherent uncertainties and dynamics of financial models related to time evolution of interest rates. We work with the Vašíček model and Cox-Ingersoll-Ross (CIR) model which describes the dynamics of interest rates over time. We incorporate the Maximum likelihood and Quasi-maximum likelihood estimation methods in estimating the parameters of our models.