  Motivated by the iron pnictides, we examine the spin excitations in an
itinerant antiferromagnet where a spin-density wave (SDW) originates from an
excitonic instability of nested electron-like and hole-like Fermi pockets.
Using the random phase approximation (RPA), we derive the Dyson equation for
the transverse susceptibility in the excitonic SDW state. The Dyson equation is
solved for two different two-band models, describing an antiferromagnetic
insulator and metal, respectively. We determine the collective spin-wave
dispersions and also consider the single-particle continua. The results for the
excitonic models are compared with each other and also contrasted with the
well-known SDW state of the Hubbard model. Despite the qualitatively different
SDW states in the two excitonic models, their magnetic response shows many
similarities. We conclude with a discussion of the relevance of the excitonic
SDW scenario to the iron pnictides.
