Properties of yield curves and forward curves for affine term structure models

Abstract

The term structure of interest rates plays the key role in pricing of bonds. Therefore its properties are interesting for many financial analysts. However in literary sources usually a sketchy description of properties of term structure occurs. In this paper an attempt of detailed description of every possible shapes of term structure is made for the class of affine interest rate models because for these models the solutions in closed form are attainable. As basis the general model (GM) with arbitrary lower boundary for interest rate is taken. The results for well-known models the CIR model and the Vasiček model are obtained as particular cases. It is found that there is four modes for yield curve shapes. The empirical evidences are presents that are based on the parameter estimates for 13 different models of real time series of yield interest rates.