A unified approach to explicit bond price solutions under a time-dependent affine term structure modelling framework
The richness and simplicity in the econometric specification of interest rate dynamics are the main motivations why affine term structure models (ATSMs) continue to be popular nowadays. Analytic solutions for bond prices are also available for some cases of these models. With explicit bond price formulae, the estimation of parameters using market data can, in principle, be carried out. In addition, with the appropriate choice of functional forms for the drift and volatility components, certain desirable features of interest rate behaviours (e.g., mean reversion, positive rates, etc.) can be captured. The desirable properties of the family of ATSMs also include the capacity to specify the distribution of the rates, their suitability for Monte Carlo simulation, and the fact that interest rate derivatives are computable from the bond prices and interest rate dynamics in a straightforward manner. It is therefore not surprising that the characterization of ATSMs has been the subject of many previous investigations in interest rate theory.