2.12 More complicated model specifications

The specific term structure model derived by CIR assumes the state of technology is represented by a single state variable, and randomness within the economy is explained by the stochastic dynamics of this variable. Hence bond prices of all maturities are determined by a single random variable, the shortterm interest rate. The model does allow some flexibility, since the term structure may assume a number of shapes , but the nature of single factor models implies that price changes in bonds of all maturities are perfectly correlated and independent of the path followed by the short-term interest rate to reach its current value.

Multi-factor models which allow a richer specification of the technology introduce more flexibility into the term structure, but often this is accompanied by an undesirable increase in complexity and lack of analytical tractability. The two models considered thus far always involve an explanatory variable that is not directly observable in the market. This is the market price of risk or factor risk premium. It is dependent on the utility function of individual investors which cannot be empirically determined. Multi-factor models will tend to have even more investor-specific, and hence unobservable, variables. At times, it may be possible to express these unobservable variables as functions of the endogenously determined prices (e.g. the risk-free rate of interest) and thereby eliminate them from the pricing model. This is the case with the Brennan and Schwartz (1979) model discussed in the next chapter.