Fitting the Yield Curve

In this chapter we consider some of the techniques used to actually fit the term structure. In theory we could use the bootstrapping approach described earlier. For a number of reasons, however, this does not produce accurate results, and so other methods are used instead. The term structure models described in the previous chapter defined the interest rate process under various assumptions about the nature of the stochastic process that drives these rates. However the zero-coupon curve derived by models such as those described by Vasicek (1977), Brennan and Schwartz (1979) and Cox, Ingersoll and Ross (1985) do not fit the observed market rates or spot rates implied by market yields, and generally market yield curves are found to contain more variable shapes than those derived using term structure models. Hence the interest rate models described in Chapter 7 are required to be calibrated to the market, and in practice they are calibrated to the market yield curve. This is carried out in two ways: either the model is calibrated to market instruments such as money market products and interest-rate swaps, which are used to construct the yield curve, or the yield curve is constructed from market instrument rates and the model is calibrated to this constructed curve. If the latter approach is preferred, there are a number of non-parametric methods that may be used. We consider these later.