Models of the Term Structure
of Bond Yields
THIS CHAPTER SURVEYS models designed for pricing term structures of market yields on default-free bonds.1 Our primary focus is on the interplay between the theoretical specification of dynamic term structure models (DTSMs) and their empirical fit to historical changes in the shapes of yield curves.2 With this interplay in mind, we characterize DTSMs in terms of three primary ingredients: the risk-neutral distribution of the state variables or risk factors, the mapping between these risk factors and the short-term interest rate, and the factor risk premiums that (when combined with the first two) allow construction of the likelihood function of the historical bond yields. Particular attention is given to affine quadratic-Gaussian, and nonaffine stochastic volatility models, and models with “regime shifts.” The goodness-of-fits of these DTSMs are assessed in Chapter 13.
There are several important segments of the fixed-income literature that we have chosen to omit from this chapter in order to keep its scope manageable. Specifically, we largely restrict our attention to dynamic pricing models that have examined features of the joint distribution of long- and short-term bond yields in estimation and testing. That is, we focus on models designed to explain the conditional distribution of yields on zero-coupon bonds with different maturities. This means that no attempt is made to systematically review the vast literature on descriptive, time-series models of interest rates (including the literature on short-term rates).3 Nor do we address the vast literature on the “forward-rate” models developed in Heath
1 This chapter is taken largely from Dai and Singleton (2003b). The pricing of defaultable fixed-income securities is taken up in Chapter 14.
2 Recent, more mathematically oriented surveys of the theoretical term structure literature can be found in Back (1996), Sundaresan (2000), Gibson et al. (2001), and Yan (2001).
3 See Chapman and Pearson (2001) for a survey with extensive coverage of empirical studies of short-rate models.