We now expand on the analysis of the term structure in chapter 3. As shown there, the term structure is best viewed as an abstract function of term to maturity, equally well described by the prices of zero coupon bonds (discount factors), yield on zero coupon bonds (spot rates) or forward rates. In the earlier case we considered two particular implementations of the term structure: A flat term structure or a term structure estimated by linear interpolations of the spot rates.
A number of alternative ways of estimating the term structure has been considered. Some are purely used as interpolation functions, while others are fully specified, dynamic term structure models. We show two examples of the first type, the approximating function proposed in Nelson and Siegel (1987) and a cubic spline used by e.g. McCulloch (1971). We also consider the term structure models of Cox et al. (1985) and Vasicek (1977).
The Cox et al. (1985) model is the most well-known example of a continous time, general equilibrium model of the term structure.