Fixed Income Markets: Management, Trading and Hedging, 2nd Edition

CHAPTER 4 Interest-Rate Modelling

In Chapter 3 we introduced basic concepts of bond interest rates and analysis. We build on these concepts in this and the next chapter, which are a review of the initial and subsequent work conducted in this field. Term-structure modelling has been extensively researched in the financial economics literature; it is possibly the most heavily covered subject in financial economics! It is not possible to deliver a comprehensive summary in just two chapters, but we aim to cover the main topics in depth. As ever, interested readers are directed to the bibliography listing, which contains the more accessible titles in this area.

In this chapter we review the more commonly used interest-rate models. In the next chapter we discuss some of the techniques used to fit a smooth yield curve to market-observed bond yields.

BACKGROUND

Term-structure modelling is based on theory describing the behaviour of interest rates. A model would seek to identify the elements or factors that are believed to explain the dynamics of interest rates. These factors are stochastic, a subset of random, in nature, so that we cannot predict with certainty the future level of any particular factor.¹ An interest-rate model must therefore specify a statistical process that describes the stochastic property of these factors, in order to arrive at a reasonably accurate representation of the behaviour of interest rates.

The first term-structure models covered in the academic literature ...