This thesis contains two papers. In the first paper, we provide a general overview of the most popular term structure of interest rate models. In order to understand different features of each model, we classify by means of general characteristics, from single-factor to multi-factor and forward rate based models. Each of these existing term structure models has its own advantages and disadvantages. We also highlight the recently advocated models in the literature: the Nelson-Siegel model, the affine and the quadratic arbitrage-free model. In the second paper we extend the affine arbitrage-free Nelson-Siegel model to a two-currency (3+1) factor structure model that incorporates the properties of interest rate term structure and foreign exchange rates simultaneously within one arbitrage-free framework by decomposing the pricing kernel into two independent portions: one portion contains three factors that model the affine Nelson-Siegel term structure of interest rate, the other portion contains one factor that captures the effect of the currency movement, which is independent of the term structure.