Chapter 8

The Evolution of Short Rates and the Shape of the Term Structure

This chapter presents a framework for understanding the shape of the term structure. In particular, it is shown how spot or forward rates are determined by expectations of future short-term rates, the volatility of short-term rates, and an interest rate risk premium. To conclude the chapter, this framework is applied to swap curves in the United States and Japan.

INTRODUCTION

From assumptions about the interest rate process for the short-term rate and from an initial term structure implied by market prices, Chapter 7 showed how to derive a risk-neutral process that can be used to price all fixed income securities by arbitrage. Models that follow this approach, i.e., models that take the initial term structure as given, are called arbitrage-free models. A different approach, however, is to start with assumptions about the interest rate process and about the risk premium demanded by the market for bearing interest rate risk and then derive the risk-neutral process. Models of this sort do not necessarily match the initial term structure and are called equilibrium models.1 The strengths and weaknesses of each approach are discussed in subsequent chapters of Part Three.

This chapter describes how assumptions about the interest rate process and about the risk premium determine the level and shape of the term structure. For equilibrium models, an understanding of the relationships between the model asssumptions ...