Fixed Income Analysis, Second Edition

CHAPTER 8

TERM STRUCTURE AND VOLATILITY OF INTEREST RATES

I. INTRODUCTION

Market participants pay close attention to yields on Treasury securities. An analysis of these yields is critical because they are used to derive interest rates which are used to value securities. Also, they are benchmarks used to establish the minimum yields that investors want when investing in a non-Treasury security. We distinguish between the on-the-run (i.e., the most recently auctioned Treasury securities) Treasury yield curve and the term structure of interest rates. The on-the-run Treasury yield curve shows the relationship between the yield for on-the-run Treasury issues and maturity. The term structure of interest rates is the relationship between the theoretical yield on zero-coupon Treasury securities and maturity. The yield on a zero-coupon Treasury security is called the Treasury spot rate. The term structure of interest rates is thus the relationship between Treasury spot rates and maturity. The importance of this distinction between the Treasury yield curve and the Treasury spot rate curve is that it is the latter that is used to value fixed-income securities.

In Chapter 6 we demonstrated how to derive the Treasury spot rate curve from the on-the-run Treasury issues using the method of bootstrapping and then how to obtain an arbitrage-free value for an option-free bond. In this chapter we will describe other methods to derive the Treasury spot rates. In addition, we explained that another ...