This study applies the nonparametric estimation procedure to the diffusion process modeling the dynamics of short-term interest rates. This approach allows us to operate in continuous time, estimating the continuous-time model, despite the use of discrete data. Three methods are proposed. We apply these methods to two important financial data. After selecting an appropriate bandwidth for each dataset, empirical comparisons indicate that the specification of the drift has a considerable impact on the pricing of derivatives through its effect on the diffusion function. In addition, a novel nonparametric test has been proposed for specification of linearity in the drift. Our simulation directs us to reject the null hypothesis of linearity at the 5% significance level for the two financial datasets.