Dynamic models of the term structure

In the past 25 years, tremendous progress has been made in modeling the dynamics of the term structure of interest rates, which play an instrumental role in determining prices and hedging portfolios of fixed-income derivative securities. This article reviews the theoretical development of the dynamic models of the default free term structure and their applications in pricing interest rate options. Classic models, sometimes termed equilibrium models, and their multifactor extensions are outlined. These models provide clear economic intuitions connecting the term structure with economic fundamentals, They also lay a foundation for the framework of the arbitrage models that price interest rate derivatives on the basis of the market prices of bonds. This framework has been expanded and enriched by recent advances in directly modeling observable market rates through the market models and in incorporating an internally consistent correlation structure through the "infinite-dimensional" models.