Term Structure Dynamics in Theory and Reality

This article is a critical survey of models designed for pricingfixed-income securities and their associated term structuresof market yields. Our primary focus is on the interplay betweenthe theoretical specification of dynamic term structure modelsand their empirical fit to historical changes in the shapesof yield curves. We begin by overviewing the dynamic term structuremodels that have been fit to treasury or swap yield curves andin which the risk factors follow diffusions, jump-diffusion,or have "switching regimes." Then the goodness-of-fit of thesemodels is assessed relative to their abilities to (i) matchlinear projections of changes in yields onto the slope of theyield curve; (ii) match the persistence of conditional volatilities,and the shapes of term structures of unconditional volatilities,of yields; and (iii) to reliably price caps, swaptions, andother fixed-income derivatives. For the case of defaultablesecurities we explore the relative fits to historical yieldspreads.