A Review of Term-Structure Models and Their Applications: [forms Part Of: Report of the Fixed-Interest Working Group, B.A.J. 4, II Pg.213–383]

The literature on ‘Term-Structure Models’ is extensive with many contributions from financial economists over the last twenty years. This paper reviews examples of term-structure models from different categories (‘equilibrium’, ‘evolutionary’ and ‘descriptive’) with particular emphasis on their intended application. The Vasicek (one-factor equilibrium), Richard (two-factor), and Hull & White (evolutionary) models are discussed in some detail. The paper reviews a particular class of descriptive polynomial models which is flexible and in widespread use both in the academic and the practitioner community. The model is cast in terms of forward rates, applied to the gilt market, and techniques are used to determine how many terms in the polynomial expansion are statistically required in order to describe the market accurately. The model is a linear model of forward and spot rates and is stable; this allows the calculation of risk measures for each bond which give a superior approach, in principle, to portfolio hedging. Selection of model should be driven by its application. If the objective is a reasonably accurate description of the curve and, by implication, an accurate indication of yields which can be obtained in the market, then a model which fits the market accurately is preferable. The ‘descriptive’ approach is therefore most appropriate in this context.