Modelling the short-term interest rate with stochastic differential equation in continuous time: linear and nonlinear models

Recently, financial engineering has brought a significant number of interest rate derivative products. Amongst the variables used in pricing these derivative products is the short-term interest rate. This research article examines various short-term interest rate models in continuous time in order to determine which model best fits the South African short-term interest rates. Both the linear and nonlinear short-term interest rate models were estimated. The methodology adopted in estimating the models was parametric approach using Quasi Maximum Likelihood Estimation (QMLE). The findings indicate that nonlinear models seem to fit the South African short-term interest rate data better than the linear model