A Review of the Dynamic Default-Free Term Structure Models

Enormous progress has been made by academics and finance practitioners alike in modeling the dynamics of the term structure of interest rates in the past 35 years. This paper extends Yan (2001). The dynamics of the term structure of interest rates are critical in assessing prices and hedging portfolios of fixed-income derivative instruments. This paper reviews the theoretical development of the dynamic models of the default-free term structure and their applications in pricing interest rate options. Equilibrium models and their multifactor extensions are examined. These models offer the economic intuition linking the term structure to economic fundamentals. These models also constitute a framework of the arbitrage models which price interest rate derivatives using the market prices of bonds. Recent studies expand this framework, directly model observable market rates, incorporate an internally consistent correlation structure, use pricing factors as observable portfolios of zero-coupon yields acting as state variables, offer a discrete time setting with recursive closed form solutions for zero coupon bonds, have unconstrained state dependence of the market prices of risk, build in smoothness restrictions on the factor loadings, and are driven by state vectors with unspanned macro risks