Dynamic models of the term structure

In the past 25 years, tremendous progress has been made in modeling the dyn amics of the term structure of interest rates, which play an instrumental r ole in determining prices and hedging portfolios of fixed-income derivative securities. This article reviews the theoretical development of the dynami c models of the default free term structure and their applications in prici ng interest rate options. Classic models, sometimes termed equilibrium mode ls, and their multifactor extensions are outlined. These models provide cle ar economic intuitions connecting the term structure with economic fundamen tals, 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 b onds. This framework has been expanded and enriched by recent advances in d irectly modeling observable market rates through the market models and in i ncorporating an internally consistent correlation structure through the "in finite-dimensional" models.