ABSTRACT
The class of affine term structure models (ATSMs) holds an important position in the literature of interest-rate derivatives models. The basic feature of ATSMs is that the short rate is an affine function of some Markov state variables; the latter can follow diffusion, jump-diffusion, or Levy dynamics. In the community of academic finance, ATSMs are often the choice of models for interest rates. There is also a huge literature on empirical studies with ATSMs. This chapter addresses the numerical implementation of the models, which makes use of fast Fourier transforms and thus represents another dimension of the numerical methodology for option pricing. According to Litterman and Scheinkman, the term structure of the interest rates is essentially driven by several factors. Because of that, three-factor models have received more attention from both researchers and practitioners. In an exponential affine model with zero-coupon bonds, yields, forward rates, and the short rate are all affine functions.
