This chapter presents an overview of the modern state of term structure modeling techniques. It provides an analytical framework that is applicable to all short rate models and considers them from the point of view of the classic approach of pricing by replication. The market price of risk and its relation to the drift of a short rate model are important considerations in modeling the term structure. The notable short rate models used in the industry for relative value pricing are introduced with a brief description of the class of affine short rate models employed for forecasting the real-world dynamics of bond prices. The chapter also includes a description of the Heath-Jarrow-Morton derivative pricing framework and an analysis of the LIBOR market model.

This chapter discusses multiple definitions of the yield curve and provides a conceptual understanding on the construction of yield curves for several markets. It reviews several definitions of the yield curve and examines the basic principles of the arbitrage-free pricing as they apply to yield curve construction. The chapter also reviews cases in which the no-arbitrage assumption is dropped from the yield curve, and then moves to specifics of the arbitrage-free curve construction for bond and swap markets. The concepts of equilibrium and market curves are introduced. The details of construction of both types of the curve are illustrated with examples from the U.S. Treasury market and the U.S. interest rate swap market. The chapter concludes by examining the major changes to the swap curve construction process caused by the financial crisis of 2007–2008 that made a profound impact on the interest rate swap markets.