Fixed-income analysis starts with the yield curve. This chapter reviews term structure fitting, which means generating a curve to represent the yield curve, the spot rate curve, the forward rate curve, or the discount function. The constructed curve should fit the data reasonably well and be sufficiently smooth. The data are either bond prices or yields, and may be raw or synthetic as prepared by reputable firms such as Salomon Brothers (now part of Citigroup).

Introduction

The yield curve consists of hundreds of dots. Because bonds may have distinct qualities in terms of tax treatment, callability, and so on, more than one yield can appear at the same maturity. Certain maturities may also lack data points. These two problems were referred to in Section 5.3 as the multiple cash flow problem and the incompleteness problem. As a result, both regression (for the first problem) and interpolation (for the second problem) are needed for constructing a continuous curve from the data.

A functional form is first postulated, and its parameters are then estimated based on bond data. Two examples are the exponential function for the discount function and polynomials for the spot rate curve [7, 317].The resulting curve is further required to be continuous or even differentiable as the relation between yield and maturity is expected to be fairly smooth. Although functional forms with more parameters often describe the data better, they are also more likely to overfit the data. An economically sensible curve that fits the data relatively well should be preferred to an economically unreasonable curve that fits the data extremely well.