Fixed Income Securities, 4th Edition

CHAPTER 8Expectations, Risk Premium, Convexity, and the Shape of the Term Structure

Chapter 7 shows how bonds and other interest rate contingent claims can be priced given the evolution of the short‐term rate. This chapter shows how the shape of the term structure of interest rates is determined by assumptions about the evolution of the short‐term rate and by assumptions about the risk premium demanded by investors for bearing interest rate risk. The first few sections of the chapter present concepts by way of example, in the simple, binomial tree framework of the previous chapter. The last section of the chapter presents the same ideas in more general setting, though at the cost of some higher‐level mathematics. Chapter 9 concludes the presentation of term structure models with a detailed description of two well‐known models.

8.1 EXPECTATIONS

Consider a simple framework with annual periods. Assume for the moment that the current one‐year rate is 8%, and that investors know with certainty that the one‐year rate in one year will be 7% and in two years will be 6%. Then, the prices of one‐, two‐, and three‐year zero coupon bonds with a unit face value, , , and , are priced such that, ...