Analysing and Interpreting the Yield Curve, 2nd Edition

CHAPTER 6Interest Rate Models II

In this chapter, we consider multi‐factor and whole yield curve models. As we noted in the previous chapter, short rate models have certain drawbacks, which though not necessarily limiting their usefulness, do not accommodate later developments. The potential shortcoming is that, as the single short rate is used to derive the complete term structure, in practice this can be unsuitable for the calculation of longer‐dated bond yields. In this situation, it becomes difficult to visualise the actual dynamics of the yield curve, and the model no longer fits observed changes in the curve. This means that the accuracy of the model cannot be observed. Another drawback is that in certain equilibrium model cases, the model cannot be fitted precisely to the observed yield curve, as it has constant parameters. In these cases, calibration of the model is on a “goodness of fit” or “best fit” approach.

In response to these issues, interest rate models have been developed that model the entire yield curve. In a whole yield curve, the dynamics of the entire term structure are modelled. In this case, the volatility of the term structure is given by a specified function, which may be a function of time, term to maturity or zero‐coupon rates. A simple approach is described in the Ho–Lee model, in which the volatility of the term structure is a parallel shift in the yield curve, the extent of which is independent of the current time and the level of current interest ...