  We revisit affine diffusion processes on general and on the canonical state
space in particular. A detailed study of theoretic and applied aspects of this
class of Markov processes is given. In particular, we derive admissibility
conditions and provide a full proof of existence and uniqueness through
stochastic invariance of the canonical state space. Existence of exponential
moments and the full range of validity of the affine transform formula are
established. This is applied to the pricing of bond and stock options, which is
illustrated for the Vasicek, Cox-Ingersoll-Ross and Heston models.
