This paper explores the structural differences and relative goodness‐of‐fits of affine term structure models (ATSMs). Within the family of ATSMs there is a trade‐off between flexibility in modeling the conditional correlations and volatilities of the risk factors. This trade‐off is formalized by our classification of N ‐factor affine family into non‐nested subfamilies of models. Specializing to three‐factor ATSMs, our analysis suggests, based on theoretical considerations and empirical evidence, that some subfamilies of ATSMs are better suited than others to explaining historical interest rate behavior.

In the setting of ‘affine’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude as well as jump timing.