This dissertation is based on the papers written by Platen and Rebolledo (1996), and Platen (1999). The papers focuses on modeling the short term interest rate by optimizing relative entropy of two probability measures Q and P. The derivation of the model is done by applying the three principles of market clearing, exclusion of arbitrage and minimization of increase of arbitrage information on a simple financial market model. The last principle is equivalent to minimization of the distance between the risk neutral and the real world probability measures. We test the model on historical data from two countries, United States and South Africa from different time frames. The results are then compared to the findings of Platen (1999). / Dissertation (MSc)--University of Pretoria, 2012. / Mathematics and Applied Mathematics / unrestricted