Fixed Income Securities, 4th Edition

CHAPTER 7Arbitrage Pricing with Term Structure Models

Principal components analysis reveals that the term structure of interest rates is determined by relatively few factors or random processes. Therefore, assumptions about how these few factors evolve over time, combined with arbitrage arguments, can deliver strong predictions about the prices and interest rate sensitivities of bonds and other interest rate contingent claims (i.e., securities with cash flows that depend on interest rates, like bond options). Formulating assumptions about the evolution of interest rate factors, pricing fixed income securities, and determining hedge ratios comprise the art and science of term structure models.

Term structure models are presented in three chapters. This chapter uses a very simple setting to show how assumptions about the evolution of the short‐term rate over time allows for the arbitrage pricing of bonds of all maturities and of interest rate contingent claims. Option‐adjusted spread (OAS) is introduced both as a metric of a security's mispricing relative to a model and as the spread that can be earned – if the model is correct – by trading that security. Chapter 8 shows how the shape of the term structure is determined by: expectations about future short‐term rates, the risk premium required by investors to bear interest rate risk, and convexity, whose effect is a result of interest rate volatility. Chapter 9 then illustrates the art of modeling the evolution of short‐term rates ...