Fixed Income Pricing

by Qiang Dai of New York University, and
Kenneth Singleton of Stanford University

July 1, 2002

Introduction: This chapter surveys the literature on fixed-income pricing models, including dynamic term structure models (DTSMs) and interest rate sensitive, derivative pricing models. This literature is vast with both the academic and practitioner communities having proposed a wide variety of models and model-selection criteria. Central to all pricing models, implicitly or explicitly, are: (i) the identity of the state vector: whether it is latent or observable and, in the latter case, which observable series; (ii) the law of motion (conditional distribution) of the state vector under the pricing measure; and (iii) the functional dependence of the short-term interest rate on this state vector. A primary objective, then, of research on fixed-income pricing has been the selection of these ingredients to capture relevant features of history, given the objectives of the modeler, while maintaining tractability, given available data and computational algorithms. Accordingly, we overview alternative conceptual approaches to fixed-income pricing, highlighting some of the tradeoffs that have emerged in the literature between the complexity of the probability model for the state, data availability, the pricing objective, and the tractability of the resulting model.

A pricing model may be "monolithic" in the sense that it prices both bonds (as functions of a set of underlying state variables or "risk factors" -- i.e., is a "term structure model") and fixed-income derivatives (with payoffs expressed in terms of the prices or yields on these underlying bonds). Alternatively, a model may be designed to price fixed-income derivatives, taking as given the current shape of the underlying yield curve. The former modeling strategy is certainly more comprehensive than the latter. However, researchers have often found that the latter approach offers more flexibility in calibration and tractability in computation when pricing certain derivatives.

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