Static Term Structure Modeling in Discrete and Continuous Time

Abstract

The term structure of interest rates represents the cost of (return from) borrowing (lending/investing) for different terms at any one moment in time. The term structure is most often specified for a specific market such as the U.S. Treasury market, the bond market for double-A rated financial institutions, the interest rate market for LIBOR and swaps, and so on. The term structure is usually specified via a rate or yield for a given term or the discount to a cash payment at some time in the future. These are often summarized mathematically through a wide variety of models. In addition, term structure models are fundamental to expressing value and risk, and establishing relative value across the spectrum of instruments found in the various interest-rate or bond markets. Static models of the term structure are characterizations that are devoted to relationships based on a given market and do not serve future scenarios where there is uncertainty. Standard static models include those known as the spot yield curve, discount function, par yield curve, and the implied forward curve. Instantiations of these models may be found in both a discrete- and continuous-time framework. An important consideration is establishing how these term structure models are constructed and how to transform one model into another. Keywords: interest rates; term structure of interest rates; term structure; market sector; market; sector; Treasuries; yield curve; discount function; spot-yield curve; par; yield; on-the-run; Qualitative theories; liquidity preference; preferred habitat; Quantitative theories; Wall Street Journal; Static models; Dynamic models; discrete-time; continuous-time; discount function; spot-yield curve; spot yield; forward rates; Equilibrium; eclectic theory; at the spot yield; spot yield